- EXPLORE Coupons Tech Help Pro Random Article About Us Quizzes Contribute Train Your Brain Game Improve Your English Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
- HELP US Support wikiHow Community Dashboard Write an Article Request a New Article More Ideas...
- EDIT Edit this Article
- PRO Courses Guides New Tech Help Pro Expert Videos About wikiHow Pro Coupons Quizzes Upgrade Sign In
- Browse Articles
- Learn Something New
- Train Your Brain
- Improve Your English
- Explore More
- Support wikiHow
- About wikiHow
- H&M Coupons
- Hotwire Promo Codes
- StubHub Discount Codes
- Ashley Furniture Coupons
- Blue Nile Promo Codes
- NordVPN Coupons
- Samsung Promo Codes
- Chewy Promo Codes
- Ulta Coupons
- Vistaprint Promo Codes
- Shutterfly Promo Codes
- DoorDash Promo Codes
- Office Depot Coupons
- adidas Promo Codes
- Home Depot Coupons
- DSW Coupons
- Bed Bath and Beyond Coupons
- Lowe's Coupons
- Surfshark Coupons
- Nordstrom Coupons
- Walmart Promo Codes
- Dick's Sporting Goods Coupons
- Fanatics Coupons
- Edible Arrangements Coupons
- eBay Coupons
- Log in / Sign up
- Education and Communications
- Mathematics
- Probability and Statistics

## How to Calculate Probability

Last Updated: October 1, 2022 References Approved

## Finding the Probability of a Single Random Event

- Example 1 : What is the likelihood of choosing a day that falls on the weekend when randomly picking a day of the week? "Choosing a day that falls on the weekend" is our event, and the number of outcomes is the total number of days in a week: 7.
- Example 2 : A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is red? "Choosing a red marble" is our event, and the number of outcomes is the total number of marbles in the jar, 20.

- Example 1 : What is the likelihood of choosing a day that falls on the weekend when randomly picking a day of the week? The number of events is 2 (since 2 days out of the week are weekends), and the number of outcomes is 7. The probability is 2 ÷ 7 = 2/7. You could also express this as 0.285 or 28.5%.
- Example 2 : A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is red? The number of events is 5 (since there are 5 red marbles), and the number of outcomes is 20. The probability is 5 ÷ 20 = 1/4. You could also express this as 0.25 or 25%.

## Calculating the Probability of Multiple Random Events

- Now, the likelihood that the second card is a club is 12/51, since 1 club will have already been removed. This is because what you do the first time affects the second. If you draw a 3 of clubs and don't put it back, there will be one less club and one less card in the deck (51 instead of 52).
- The probability that the first marble is red is 5/20, or 1/4. The probability of the second marble being blue is 4/19, since we have 1 less marble, but not 1 less blue marble. And the probability that the third marble is white is 11/18, because we’ve already chosen 2 marbles.

- Example 1 : Two cards are drawn randomly from a deck of cards. What is the likelihood that both cards are clubs? The probability of the first event happening is 13/52. The probability of the second event happening is 12/51. The probability is 13/52 x 12/51 = 12/204 = 1/17. You could also express this as 0.058 or 5.8%.
- Example 2 : A jar contains 4 blue marbles, 5 red marbles and 11 white marbles. If three marbles are drawn from the jar at random, what is the probability that the first marble is red, the second marble is blue, and the third is white? The probability of the first event is 5/20. The probability of the second event is 4/19. And the probability of the third event is 11/18. The probability is 5/20 x 4/19 x 11/18 = 44/1368 = 0.032. You could also express this as 3.2%.

## Converting Odds to Probabilities

- The number 11 represents the likelihood of choosing a white marble and the number 9 represents the likelihood of choosing a marble of a different color.
- So, odds are that you will draw a white marble.

## Probability Cheat Sheets

## Expert Q&A Did you know you can get premium answers for this article? Unlock premium answers by supporting wikiHow

Support wikiHow by unlocking this expert answer.

Support wikiHow by unlocking this staff-researched answer.

## Video . By using this service, some information may be shared with YouTube.

- Mathematicians typically use the term “relative probability” to refer to the chances of an event happening. They insert the word "relative" since no outcome is 100% guaranteed. For example, if you flip a coin 100 times, you probably won't get exactly 50 heads and 50 tails. Relative probability takes this caveat into account. [10] X Research source ⧼thumbs_response⧽ Helpful 0 Not Helpful 2
- You may need to know that that in sports betting and bookmaking, odds are expressed as “odds against,” which means that the odds of an event happening are written first, and the odds of an event not happening come second. Although it can be confusing, it's important to know this if you’re planning to bet on a sporting event. ⧼thumbs_response⧽ Helpful 10 Not Helpful 4
- The most common ways of writing down probabilities include putting them as fractions, as decimals, as percentages, or on a 1–10 scale. ⧼thumbs_response⧽ Helpful 7 Not Helpful 5

## You Might Also Like

- ↑ https://www.theproblemsite.com/reference/mathematics/probability/mutually-exclusive-outcomes
- ↑ Mario Banuelos, PhD. Assistant Professor of Mathematics. Expert Interview. 11 December 2021.
- ↑ https://www.mathplanet.com/education/pre-algebra/probability-and-statistic/probability-of-events
- ↑ https://www.mathsisfun.com/probability_line.html
- ↑ https://www.probabilisticworld.com/not-all-zero-probabilities/
- ↑ https://www.wyzant.com/resources/lessons/math/statistics_and_probability/probability/further_concepts_in_probability
- ↑ https://www.intmath.com/counting-probability/8-independent-dependent-events.php
- ↑ https://www.bbc.com/bitesize/guides/zsrq6yc/revision/3

## About This Article

## Reader Success Stories

## Did this article help you?

## Featured Articles

## Trending Articles

## Watch Articles

- + ACCUPLACER Mathematics
- + ACT Mathematics
- + AFOQT Mathematics
- + ALEKS Tests
- + ASVAB Mathematics
- + ATI TEAS Math Tests
- + Common Core Math
- + DAT Math Tests
- + FSA Tests
- + FTCE Math
- + GED Mathematics
- + Georgia Milestones Assessment
- + GRE Quantitative Reasoning
- + HiSET Math Exam
- + HSPT Math
- + ISEE Mathematics
- + PARCC Tests
- + Praxis Math
- + PSAT Math Tests
- + PSSA Tests
- + SAT Math Tests
- + SBAC Tests
- + SIFT Math
- + SSAT Math Tests
- + STAAR Tests
- + TABE Tests
- + TASC Math
- + TSI Mathematics
- + ACT Math Worksheets
- + Accuplacer Math Worksheets
- + AFOQT Math Worksheets
- + ALEKS Math Worksheets
- + ASVAB Math Worksheets
- + ATI TEAS 6 Math Worksheets
- + FTCE General Math Worksheets
- + GED Math Worksheets
- + 3rd Grade Mathematics Worksheets
- + 4th Grade Mathematics Worksheets
- + 5th Grade Mathematics Worksheets
- + 6th Grade Math Worksheets
- + 7th Grade Mathematics Worksheets
- + 8th Grade Mathematics Worksheets
- + 9th Grade Math Worksheets
- + HiSET Math Worksheets
- + HSPT Math Worksheets
- + ISEE Middle-Level Math Worksheets
- + PERT Math Worksheets
- + Praxis Math Worksheets
- + PSAT Math Worksheets
- + SAT Math Worksheets
- + SIFT Math Worksheets
- + SSAT Middle Level Math Worksheets
- + 7th Grade STAAR Math Worksheets
- + 8th Grade STAAR Math Worksheets
- + THEA Math Worksheets
- + TABE Math Worksheets
- + TASC Math Worksheets
- + TSI Math Worksheets
- + AFOQT Math Course
- + ALEKS Math Course
- + ASVAB Math Course
- + ATI TEAS 6 Math Course
- + CHSPE Math Course
- + FTCE General Knowledge Course
- + GED Math Course
- + HiSET Math Course
- + HSPT Math Course
- + ISEE Upper Level Math Course
- + SHSAT Math Course
- + SSAT Upper-Level Math Course
- + PERT Math Course
- + Praxis Core Math Course
- + SIFT Math Course
- + 8th Grade STAAR Math Course
- + TABE Math Course
- + TASC Math Course
- + TSI Math Course
- + Number Properties Puzzles
- + Algebra Puzzles
- + Geometry Puzzles
- + Intelligent Math Puzzles
- + Ratio, Proportion & Percentages Puzzles
- + Other Math Puzzles

## How to Solve Probability Problems? (+FREE Worksheet!)

## Related Topics

- How to Interpret Histogram
- How to Interpret Pie Graphs
- How to Solve Permutations and Combinations
- How to Find Mean, Median, Mode, and Range of the Given Data

## Step by step guide to solve Probability Problems

- Probability is the likelihood of something happening in the future. It is expressed as a number between zero (can never happen) to \(1\) (will always happen).
- Probability can be expressed as a fraction, a decimal, or a percent.
- To solve a probability problem identify the event, find the number of outcomes of the event, then use probability law: \(\frac{number\ of \ favorable \ outcome}{total \ number \ of \ possible \ outcomes}\)

## Probability Problems – Example 1:

## Probability Problems – Example 2:

## Exercises for Solving Probability Problems

- A number is chosen at random from \(1\) to \(10\). Find the probability of selecting a \(4\) or smaller.
- A number is chosen at random from \(1\) to \(50\). Find the probability of selecting multiples of \(10\).
- A number is chosen at random from \(1\) to \(10\). Find the probability of selecting of \(4\) and factors of \(6\).
- A number is chosen at random from \(1\) to \(10\). Find the probability of selecting a multiple of \(3\).
- A number is chosen at random from \(1\) to \(50\). Find the probability of selecting prime numbers.
- A number is chosen at random from \(1\) to \(25\). Find the probability of not selecting a composite number.

## Download Probability Problems Worksheet

- \(\color{blue}{\frac{2}{5}}\)
- \(\color{blue}{\frac{1}{10}}\)
- \(\color{blue}{\frac{1}{2}}\)
- \(\color{blue}{\frac{3}{10}}\)
- \(\color{blue}{\frac{9}{25}}\)

by: Reza about 3 years ago (category: Articles , Free Math Worksheets )

## Related to This Article

- Top 10 HSPT Math Practice Questions
- How to Use Number Lines to Identify Equivalent Fractions?
- How to Graph Trigonometric Functions?
- Number Properties Puzzle – Challenge 13
- Word Problems Involving Writing a Ratio
- 6th Grade OST Math Practice Test Questions
- Is the CBEST Math Difficult?
- How to Add and Subtract Polynomials Using Algebra Tiles
- FREE DAT Quantitative Reasoning Math Practice Test
- How to Find the Perimeter of Polygons? (+FREE Worksheet!)

## What people say about "How to Solve Probability Problems? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?

## Leave a Reply Cancel reply

You must be logged in to post a comment.

## STAAR Algebra I for Beginners The Ultimate Step by Step Guide to Acing STAAR Algebra I

It was $16.99 now it is $11.99

## Login and use all of our services.

Effortless Math services are waiting for you. login faster!

## Register Fast!

Password will be generated automatically and sent to your email.

After registration you can change your password if you want.

- Math Worksheets
- Math Courses
- Math Topics
- Math Puzzles
- Math eBooks
- GED Math Books
- HiSET Math Books
- ACT Math Books
- ISEE Math Books
- ACCUPLACER Books
- Premium Membership
- Youtube Videos
- Google Play
- Apple Store

- Android App Development (Live)
- Data Science (Live)
- DSA for Interview Preparation
- DSA Live for Working Professionals
- DSA Self-paced in C++/Java
- DSA Self-paced in Python
- DSA Self-paced in Javascript
- DSA Self-paced in C
- Data Structure & Algorithm Classes (Live)
- System Design (Live)
- DevOps(Live)
- Data Structures & Algorithms in JavaScript
- Explore More Live Courses
- Interview Preparation Course
- GATE CS & IT 2024
- Data Structure & Algorithm-Self Paced(C++/JAVA)
- Data Structures & Algorithms in Python
- Explore More Self-Paced Courses
- C++ Programming - Beginner to Advanced
- Java Programming - Beginner to Advanced
- C Programming - Beginner to Advanced
- Full Stack Development with React & Node JS(Live)
- Java Backend Development(Live)
- Android App Development with Kotlin(Live)
- Python Backend Development with Django(Live)
- Complete Data Science Program(Live)
- Mastering Data Analytics
- DevOps Engineering - Planning to Production
- CBSE Class 12 Computer Science
- School Guide
- All Courses
- Singly Linked List
- Doubly Linked List
- Circular Linked List
- Doubly Circular linked list
- Generic Tree
- Binary Tree
- Binary Search Tree
- Red Black Tree
- All Tree Data Structures
- Set Data Structure
- Map Data Structure
- Advanced Data Structure
- All Data Structures
- Design and Analysis of Algorithms
- Asymptotic Analysis
- Worst, Average and Best Cases
- Asymptotic Notations
- Little o and little omega notations
- Lower and Upper Bound Theory
- Analysis of Loops
- Solving Recurrences
- Amortized Analysis
- What does 'Space Complexity' mean ?
- Pseudo-polynomial Algorithms
- Polynomial Time Approximation Scheme
- A Time Complexity Question
- Linear Search
- Binary Search
- All Searching Algorithms
- Selection Sort
- Bubble Sort
- Insertion Sort
- Counting Sort
- Bucket Sort
- All Sorting Algorithms
- Greedy Algorithms
- Dynamic Programming
- Graph Algorithms
- Pattern Searching
- Backtracking
- Divide and Conquer
- Geometric Algorithms
- Mathematical
- Bitwise Algorithms
- Randomized Algorithms
- Branch and Bound
- All Algorithms
- What is System Design
- Key Terminologies in System Design
- Analysis and Architecture of Systems
- Scalability in System Design
- Databases in System Design
- High Level Design or HLD
- Low Level Design or LLD
- Communication Protocols
- Web Servers and Proxies
- Case Studies in Designing Systems
- Complete System Design Tutorial
- Factory Pattern
- Observer Pattern
- Singleton Design Pattern
- Decorator Pattern
- Strategy Pattern
- Adapter Pattern
- Command Pattern
- Iterator Pattern
- Prototype Design Pattern
- All Design Patterns
- Company Preparation
- Practice Company Questions
- Interview Experiences
- Experienced Interviews
- Internship Interviews
- Competitive Programming
- Multiple Choice Quizzes
- Aptitude for Placements
- Go Language
- Tailwind CSS
- Foundation CSS
- Materialize CSS
- Semantic UI
- Angular PrimeNG
- Angular ngx Bootstrap
- jQuery Mobile
- jQuery EasyUI
- React Bootstrap
- React Rebass
- React Desktop
- React Suite
- ReactJS Evergreen
- ReactJS Reactstrap
- BlueprintJS
- TensorFlow.js
- English Grammar
- School Programming
- Number System
- Trigonometry
- Probability
- Mensuration
- Class 8 Syllabus
- Class 9 Syllabus
- Class 10 Syllabus
- Class 11 Syllabus
- Class 12 Syllabus
- Class 8 Notes
- Class 9 Notes
- Class 10 Notes
- Class 11 Notes
- Class 12 Notes
- Class 8 Formulas
- Class 9 Formulas
- Class 10 Formulas
- Class 11 Formulas
- Class 8 Maths Solution
- Class 9 Maths Solution
- Class 10 Maths Solution
- Class 11 Maths Solution
- Class 12 Maths Solution
- Class 7 SS Syllabus
- Class 8 SS Syllabus
- Class 9 SS Syllabus
- Class 10 SS Syllabus
- Class 7 Notes
- History Class 7
- History Class 8
- History Class 9
- Geo. Class 7
- Geo. Class 8
- Geo. Class 9
- Civics Class 7
- Civics Class 8
- Business Studies (Class 11th)
- Microeconomics (Class 11th)
- Statistics for Economics (Class 11th)
- Business Studies (Class 12th)
- Accountancy (Class 12th)
- Macroeconomics (Class 12th)
- Political Science
- Machine Learning
- Data Science
- Microsoft Azure Tutorial
- Google Cloud Platform
- Mathematics
- Operating System
- Computer Networks
- Computer Organization and Architecture
- Theory of Computation
- Compiler Design
- Digital Logic
- Software Engineering
- GATE 2024 Live Course
- GATE Computer Science Notes
- Last Minute Notes
- GATE CS Solved Papers
- GATE CS Original Papers and Official Keys
- GATE CS 2023 Syllabus
- Important Topics for GATE CS
- GATE 2023 Important Dates
- ISRO CS Original Papers and Official Keys
- ISRO CS Solved Papers
- ISRO CS Syllabus for Scientist/Engineer Exam
- UGC NET CS Notes Paper II
- UGC NET CS Notes Paper III
- UGC NET CS Solved Papers
- HTML Cheat Sheet
- CSS Cheat Sheet
- Bootstrap Cheat Sheet
- JS Cheat Sheet
- jQuery Cheat Sheet
- Angular Cheat Sheet
- Facebook SDE Sheet
- Amazon SDE Sheet
- Apple SDE Sheet
- Netflix SDE Sheet
- Google SDE Sheet
- Wipro Coding Sheet
- Infosys Coding Sheet
- TCS Coding Sheet
- Cognizant Coding Sheet
- HCL Coding Sheet
- FAANG Coding Sheet
- Love Babbar Sheet
- Mass Recruiter Sheet
- Product-Based Coding Sheet
- Company-Wise Preparation Sheet
- Array Sheet
- String Sheet
- Graph Sheet
- Geography Notes
- Modern Indian History Notes
- Medieval Indian History Notes
- Ancient Indian History Notes
- Complete History Notes
- Science & Tech. Notes
- Ethics Notes
- Polity Notes
- Economics Notes
- Government Schemes (Updated)
- UPSC Previous Year Papers
- Campus Ambassador Program
- School Ambassador Program
- Geek of the Month
- Campus Geek of the Month
- Placement Course
- Testimonials
- Student Chapter
- Geek on the Top
- SSC CGL Syllabus
- General Studies
- Subjectwise Practice Papers
- Previous Year Papers
- SBI Clerk Syllabus
- General Awareness
- Quantitative Aptitude
- Reasoning Ability
- SBI Clerk Practice Papers
- SBI PO Syllabus
- SBI PO Practice Papers
- IBPS PO 2022 Syllabus
- English Notes
- Reasoning Notes
- Mock Question Papers
- IBPS Clerk Syllabus
- Corporate Hiring Solutions
- Apply through Jobathon
- Apply for a Job
- All DSA Problems
- Problem of the Day
- GFG SDE Sheet
- Top 50 Array Problems
- Top 50 String Problems
- Top 50 Tree Problems
- Top 50 Graph Problems
- Top 50 DP Problems
- GFG Weekly Coding Contest
- Job-A-Thon: Hiring Challenge
- BiWizard School Contest
- All Contests and Events
- Saved Videos
- What's New ?
- Current Affairs
- General Knowledge
- SSC CGL Pre.Yrs.Papers
- SSC CGL Practice Papers
- SBI Clerk PYQ
- IBPS PO PYQ
- IBPS Clerk PYQ
- SBI PO Practice Paper

## Related Articles

- Write an Interview Experience
- Write an Admission Experience
- Quantitative Aptitude For IBPS PO Exam
- Simplification and Approximation
- Approximation – Aptitude Question and Answers
- Practice Set For Profit and Loss
- Profit and Loss
- Mixture and Alligation | Set 2
- Tricks To Solve Mixture and Alligation
- Mixtures and Alligation

## Tricks To Solve Probability Questions

- Simple Interest
- Compound Interest Formula
- Time And Work
- Speed and Distance Advance Level
- Mensuration 2D
- Geometry and Co-ordinates
- Coordinate Geometry
- Ratios and Percentages
- Ratio and Proportions Formula
- Basic Concept of Percentage
- Tips & Tricks To Solve Ratio & Proportion – Advance Level
- What is a number system?
- Number System in Maths
- Basic Concept Of Number System
- Special Series – Sequences and Series | Class 11 Maths
- Permutation and Combination
- Permutation
- Tricks To Solve Questions On Average
- Quadratic Formula
- Roots of Quadratic Equations
- Relationship Between Two Variables
- Data Sufficiency
- Important Formulas of Interest, Mensuration, Permutation & Combination and Probability
- Arithmetic Progression
- Practice Set For Height & Distance

The application or uses of probability can be seen in quantitative aptitude as well as in daily life. It is needful to learn the basic concept of probability. We will cover the basics as well as the hard level problems for all levels of students for all competitive exams especially SBI PO, SBI CLERK, IBPS PO, IBPS CLERK, RRB PO, NICL AO, LIC AAO, SNAP, MAT, SSC CGL etc.

Types of questions asked in the competitive exam:

1. Question A coin is thrown two times .what is the probability that at least one tail is obtained?

A) 3/4 B) 1/4 C) 1/3 D) 2/3 E) None of these

Sample space = [TT, TH, HT,HH] Total number of ways = 2 × 2 = 4. Favourite Cases = 3 P (A) = 3/4

Tricks:- P (of getting at least one tail) = 1 – P (no head)⇒ 1 – 1/4 = 3/4

2. Question What is the probability of getting a numbered card when drawn from the pack of 52 cards?

A) 1/13 B) 1/9 C) 9/13 D) 11/13 E) None of these

A) 1/35 B) 35/132 C) 1/132 D) 35/144 E) None of these

P (B) × P (P) = (5/12) x (7/11) = 35/132

4.Question Find the probability of getting a sum of 8 when two dice are thrown?

A) 1/8 B) 1/5 C) 1/4 D) 5/36 E) 1/3

A) 4/13 B) 1/3 C) 5/12 D) 7/52 E) None of these

A) 1/13 B) 2/13 C) 3/13 D) 4/13 E) 5/13

7.Question If two dice are rolled together then find the probability as getting at least one ‘3’?

A) 11/36 B) 1/12 C) 1/36 D) 13/25 E) 13/36

8. Question If a single six-sided die is rolled then find the probability of getting either 3 or 4.

A) 1/2 B) 1/3 C) 1/4 D) 2/3 E) 1/6

A) 1/10 B) 3/10 C) 7/10 D) 9/10 E) None of these

A) 5/21 B) 3/23 C) 5/63 D) 19/63 E) None of these

A) 1/4 B) 3/10 C) 1/3 D) 2/3 E) None of these

Here, the total number of boys = 15 and the total number of girls = 15

Probability of choosing A grade student= 9/30

Now, an A-grade student chosen can be a girl. So the probability of choosing it = 4/30

A) 2/13 B) 3/13 C) 4/13 D) 5/23 E) None of these

Answer:- C Sol: There are 4 aces in a pack, 13 club cards and 1 ace of club card.

Now, the probability of getting an ace = 4/52

Probability of getting a club = 13/52

Probability of getting an ace of club = 1/52

Required probability of getting an ace or a club

= 4/52 + 13/52 – 1/52 = 16/52 = 4/13

A) 12/13 B) 3/13 C) 7/13 D) 5/23 E) None of these

Well-shuffling ensures equally likely outcomes. Total king of a deck = 4

The number of favourable outcomes F= 52 – 4 = 48

The number of possible outcomes = 52

Therefore, the required probability

14.Question If P(A) = 7/13, P(B) = 9/13 and P(A∩B) = 4/13, find the value of P(A|B).

A) 1/9 B) 2/9 C) 3/9 D) 4/9 E) None of these

P(A|B) = P(A∩B)/P(B) = (4/13)/(9/13) = 4/9.

15. Question A one rupee coin and a two rupee coin are tossed once, then calculate a sample space.

The outcomes are either Head (H) or tail(T).

Now,heads on both coins = (H,H) = HH

Tails on both coins = ( T, T) = TT

Probability of head on one rupee coin and Tail on the two rupee coins = (H, T) = HT

And Tail on one rupee coin and Head on the two rupee coin = (T, H) = TH

Thus, the sample space ,S = [HH, HT, TH, TT]

A) 1/4 B) 2/13 C) 8/15 D) 9/20 E) None of these

Here, S = {1, 2, 3, 4, …., 19, 20} = 20

Multiples of 4: 4, 8, 12, 16, 20 (5 tickets) Multiples of 5: 5, 10, 15, 20 (4 tickets)

Total number of tickets with numbers that are multiples of 4 or 5: 5 + 4 – 1 = 8

18 ) he likes either chicken or mutton

19 ) he likes neither fish nor mutton.

The total number of favourable outcomes = 300 (Since there are 300 students altogether).

The number of times a chicken liker is chosen = 95 (Since 95 students like chicken).

The number of times a fish liker is chosen = 120.

The number of times a mutton liker is chosen = 80.

The number of times a student is chosen who likes none of these = 5.

17. Question Find the probability that the student like mutton?

A) 3/10 B) 4/15 C) 1/10 D) 1/15 E) None of these

Therefore, the probability of getting a student who likes mutton

18. Question What is the probability that the student likes either chicken or mutton?

A) 7/12 B) 5/12 C) 3/4 D) 1/12 E) None of these

19. Question Find the probability that the student likes neither fish nor mutton.

A) 1/2 B) 1/5 C) 1/3 D) 1/4 E) 1/6

20) The number is a two-digit number

21) The number is a perfect square

22) The number is a multiply of 5

20. Question Find the probability that the number is a two-digit number.

A) 1/9 B) 1/10 C) 9/10 D) 7/10 E) None of these

21. Question What is the probability that the number is a perfect square?

A) 1/9 B) 1/10 C) 9/10 D) 1/7 E) None of these

22.Question Find the probability that the number is a multiple of 5.

A) 1/5 B) 1/6 C) 1/10 D) 1/8 E) 9/10

Thus, the required probability= 18/90 =1/5

## Please Login to comment...

- harendrakumar123
- atulyadavche19
- Banking Practice Paper
- Banking Quantitative Aptitude
- SSC Practice Paper
- SSC Quantitative Aptitude
- SSC/Banking

## Complete Test Series for Service-Based Companies

## Complete Interview Preparation - Self Paced

## System Design - Live

Improve your coding skills with practice.

- All Platforms
- First Naukri
- All Companies
- Cognizant GenC
- Cognizant GenC Next
- Cognizant GenC Elevate
- Goldman Sachs
- Infosys SP and DSE
- TCS CodeVita
- TCS Digital
- TCS iON CCQT
- TCS Smart Hiring
- Tech Mahindra
- Zs Associates

- Top 100 Codes
- Learn Python
- Learn Data Structures
- Learn Competitve & Advanced Coding
- Learn Operating System
- Software Engineering
- Online Compiler
- Microsoft Coding Questions
- Amazon Coding Questions

- Interview Preparation
- HR Interview
- Virtual Interview
- Technical Interview
- Group Discussions
- Leadership Questions

- Get OffCampus updates
- On Instagram
- On LinkedIn
- On Telegram
- On Whatsapp
- AMCAT vs CoCubes vs eLitmus vs TCS iON CCQT
- Companies hiring via TCS iON CCQT
- Companies hiring via CoCubes
- Companies hiring via AMCAT
- Companies hiring via eLitmus
- Companies hiring from AMCAT, CoCubes, eLitmus
- Prime Video
- Interview Experience
- Prime Video New
- Interview Prep
- Nano Degree

## How To Solve Probability Questions Quickly

## How to Solve Proabability Questions Quickly

Here , In this Page you learn Find How to Solve Probability Questions Quickly.

Therefore, probability of the occurrence of event is the number between 0 and 1 .

## How to Solve Quickly Probability questions

- You can solve many simple probability problems just by knowing two simple rules:
- The probability of any sample point can range from 0 to 1.
- The sum of probabilities of all sample points in a sample space is equal to 1.
- The probability of event A is denoted by P(A).

## Types 1- How to Solve Probability Questions Quickly of Random ticket or ball drawn

Solution: Here, S = {1, 2, 3, 4, …., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) = \frac{n(E)}{n(S)} = \frac{9}{20}

Solution: Total number of balls = (2 + 3 + 2) = 7.

Then, n (S) = Number of ways of drawing 2 balls out of 7.

Let E = Event of drawing 2 balls, none of which is blue.

P(E) = \frac{n(E)}{n(S)} = \frac{10}{21} .

Solution: Ticket has a maximum of 4 digits on it as Thousands, Hundreds Tens ,Units or TH H T U.

Number of Tickets with 2 in TH place = 0.

Number of Tickets with 2 in H place = From 200 upto 299 = 100.

Number of Tickets with 2 ONLY in U place but not in TH H or T place

= H or T place both have (0 to 9 excluding 2) + (TH=1 & H=0 & U

= 2 & (T= 0 to 9 excluding 2) )

Total Tickets with at least one 2 = 290

Probability = \frac{290}{1100} is answer.

- Formulas to solve probability questions
- Tips and Tricks of Probability
- Questions and Answers of Probability

## Type 2- How to Solve Probability Questions Quickly of boys and girls

Solutions : Assume total students in the class = 100

Solution : Let A= first die is 5

Let B = total of two dice is greater than 9

P( A ) = Possible outcomes for A and B : (5, 5), (5, 6)

P(A and B) = \frac{2}{36} = \frac{1}{18}

P(B|A) = \frac{P(A and B)}{P(A)} = \frac{1}{18} ÷ \frac{1}{6} = \frac{1}{3} .

Alternatively, one can solve the problem directly using counting techniques.

Total = arrangements with Archie, Jerry or Moose in the aisle seat.

Number of options for the aisle seat = 3. (Archie, Jughead, or Moose)

Number of ways to arrange the 4 other people = 4 x 3 x 2 x 1.

To combine these options, we multiply: 3 x 4 x 3 x 2 = 72.

Bad = arrangements with Archie, Jerry or Moose in the aisle seat BUT with Betty next to Veronica.

Number of options for the aisle seat = 3. (Archie, Jughead, Moose).

Number of ways to arrange the 2 remaining people = 2 x 1.

To combine these options, we multiply: 3 x 2 x 2 x 2 = 24.

Good arrangements = 72 – 24 = 48.

## Prime Course Trailer

## Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

## Get over 200+ course One Subscription

## Checkout list of all the video courses in PrepInsta Prime Subscription

- Permutation & Combination – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Combination – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Circular Permutation – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Permutation & Combination – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Combination – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

## Free Mathematics Tutorials

Probability questions with solutions.

## Questions and their Solutions

Answers to above exercises, more references and links, popular pages.

- Statistics and Probability Problems with Solutions - sample 3
- Math Word Problems with Answers - Grade 8
- Math Problems, Questions and Online Self Tests
- High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
- Free Algebra Questions and Problems with Answers
- Privacy Policy

## Sciencing_Icons_Science SCIENCE

## How to Solve Probability Questions

## How to Explain the Sum & Product Rules of Probability

## Related Articles

Thinkstock/Comstock/Getty Images

## Find Your Next Great Science Fair Project! GO

We Have More Great Sciencing Articles!

## Solve probability, percentile, and more

= the average of the 49 races.

a. Give the distribution of X .

(Round your standard deviation to two decimal places.)

d. Find the median of the average running times.

## 1 Expert Answer

MS in Statistics with 5+ years of tutoring experience

P(146<X<149) = P( (146-147)/(15/7) < Z < (149-147)/(15/7) ) go from here/. LMK if you need more help

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem. Most questions answered within 4 hours.

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

## RELATED TOPICS

Related questions, how do i create a probability model.

## Statistics with chi square

## RECOMMENDED TUTORS

## find an online tutor

- Statistics tutors
- Multivariate Statistics tutors
- Psychological Statistics tutors
- Statistics Graduate Level tutors
- Statistical Inference tutors
- Probability tutors
- Math tutors
- Data Analysis tutors

## related lessons

- Introduction to Statistics
- Hypothesis testing
- Preparing for the 2016 SAT Changes
- SAT Math Test Format and Strategies
- GRE Quant Test Format and Strategies
- Statements of Cash Flows
- SAT Overview and Format

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

## Statistics and probability

Course: statistics and probability > unit 7, calculating conditional probability.

- Conditional probability explained visually
- Conditional probability using two-way tables
- Conditional probability tree diagram example
- Tree diagrams and conditional probability
- Conditional probability and independence
- Analyzing event probability for independence

## Want to join the conversation?

## Video transcript

Teaching support from the UK’s largest provider of in-school maths tuition.

Hundreds of FREE online maths resources!

Daily activities, ready-to-go lesson slides, SATs revision packs, video CPD and more!

## 15 Probability Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

## Beki Christian

## What are some real life examples of probability?

The probability of something happening is given by:

We can also use the following formulae to help us calculate probabilities and solve problems:

- Probability of something not occuring = 1 – probability of if occurring P(not\;A) = 1 - P(A)
- For mutually exclusive events: Probability of event A OR event B occurring = Probability of event A + Probability of event B P(A\;or\;B) = P(A)+P(B)
- For independent events: Probability of event A AND event B occurring = Probability of event A times probability of event B P(A\;and\;B) = P(A) × P(B)

## KS3 probability questions

A and E are vowels so there are 2 outcomes that are vowels out of 6 outcomes altogether.

Therefore the probability is \frac{2}{6} which can be simplified to \frac{1}{3} .

What is the relative frequency of the coin landing on heads?

Max tossed the coin 67 times and it landed on heads 26 times.

What did Grace do with the two numbers shown on the dice?

Subtract the number on dice 2 from the number on dice 1

Subtract the smaller number from the bigger number

For each pair of numbers, Grace subtracted the smaller number from the bigger number.

For example, if she rolled a 2 and a 5, she did 5 − 2 = 3.

Since the probability of mutually exclusive events add to 1:

\begin{aligned} x+4x&=1\\\\ 5x&=1\\\\ x&=\frac{1}{5} \end{aligned}

\frac{1}{5} of the balls are red and \frac{4}{5} of the balls are blue.

How many students don’t like science?

## KS4 probability questions

7. A restaurant offers the following options:

Main – chicken, fish or vegetarian

How many possible different combinations of starter, main and dessert are there?

The number of different combinations is 2 × 3 × 2 = 12.

First we need to work out how many students walk to school:

\frac{2}{9} \text{ of } 18 = 4

\frac{1}{4} \text{ of } 12 = 3

Let’s call the probability of getting a head p.

The probability p, of getting a head AND getting another head is 0.16.

The probability of getting a head is 0.4 so the probability of getting a tail is 0.6.

The probability of getting two tails is 0.6 × 0.6 = 0.36 .

If I were to pick 60 jelly beans from the tub, how many orange jelly beans would I expect to pick?

The probability of picking an orange is 0.25.

The number of times I would expect to pick an orange jelly bean is 0.25 × 60 = 15 .

Probability of winning is \frac{1}{2} \times \frac{4}{13} = \frac{4}{26}

If 260 play the game, Dexter would receive £260.

The expected number of winners would be \frac{4}{26} \times 260 = 40

Dexter would need to give away 40 × £3 = £120 .

Therefore Dexter’s profit would be £260 − £120 = £140.

12. A coin is tossed three times. Work out the probability of getting two heads and one tail.

There are three ways of getting two heads and one tail: HHT, HTH or THH.

The probability of each is \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}

Therefore the total probability is \frac{1}{8} +\frac{1}{8} + \frac{1}{8} = \frac{3}{8}

Since we know that the person chose 100m, we need to include the people in that column only.

In total 88 people chose 100m so the probability the person was female is \frac{32}{88} .

14. Sam asked 50 people whether they like vegetable pizza or pepperoni pizza.

37 people like vegetable pizza.

We need to draw a venn diagram to work this out.

To get one red and one blue, Nico could choose red then blue or blue then red so the probability is:

Take a look at the probability lessons today – more are added every week.

- 25 GCSE maths questions
- 15 Ratio questions
- 15 Algebra questions
- 15 Trigonometry questions
- 15 Simultaneous equations questions
- 15 Venn diagram questions
- 15 Pythagoras theorem questions
- Long division questions

## Download this 15 Probability Questions And Practice Problems (KS3 & KS4) Worksheet

## FREE GCSE Circle Theorems Worksheet

## Privacy Overview

## Stack Exchange Network

Connect and share knowledge within a single location that is structured and easy to search.

## How to solve Probability questions? [closed]

I am preparing GRE Test which has Math Part.

How to solve probability questions in a real quick ?

## 3 Answers 3

I assume you mean the bag contains 4 black marbles.

I am assuming you meant the bag "contains 4 black marbles, ..."

## Not the answer you're looking for? Browse other questions tagged probability .

- Featured on Meta
- AI/ML Tool examples part 3 - Title-Drafting Assistant
- We are graduating the updated button styling for vote arrows

## Hot Network Questions

- Can statistical units measured per thousand inhabitants be bigger than 1000?
- Can you pack these tetracubes to form a rectangular block with at least one odd side length?
- Partial derivatives vs Covariant derivatives in polar coordinates
- Date Checking in C++
- Who said that one should change one’s direction of research every seven years?
- Why doesn't vocal music use C clefs nowadays?
- What is the simple dependence of the diagonals (or columns) of the Faulhaber matrix on the first entry (Bernoulli numbers)?
- Why do capacitors in series have same charge?
- Faithful representations of integral models
- What exactly are Avoid Notes?
- How do I make sure that a hook is not misinterpreted as a writing mistake or plot holes?
- What is the longest bridge that a Bronze Age society could put together?
- Why the passive "are described" is not grammatically correct in this sentence
- How may a titlepage be colored?
- Numbers of combinations modulo m, efficiently
- Why did it take so long to invent telescopes given glass was used 4000 years ago in Mesopotamia?
- How to make bash keyboard editing default to vi from emacs?
- I’d rather come or go with you
- Using a foreign passport in the UK as a British citizen
- 40A GFCI Breaker keeps tripping when charging EV after about 1.5 hours
- Are legislators ever asked to explain their intent in Supreme Court cases?
- Why is deploying nuclear weapons in Belarus seen as a problem, and how would this help Russia?
- union of constraints
- How to change the casefold ext4 filesystem option of the root partition, if I only have ssh access

## Probability Questions

The probability of happening of an event E is a number P(E) such that:

Probability Formula: If an event E occurs, then the empirical probability of an event to happen is:

P(E) = Number of trials in which Event happened/Total number of trials

The theoretical probability of an event E, P(E), is defined as:

P(E) = (Number of outcomes favourable to E)/(Number of all possible outcomes of the experiment)

## Probability Questions & Answers

1. Two coins are tossed 500 times, and we get:

Find the probability of each event to occur.

The Sum of probabilities of all elementary events of a random experiment is 1.

P(E 1 )+P(E 2 )+P(E 3 ) = 0.21+0.55+0.24 = 1

If a tyre is bought from this company, what is the probability that :

(i) it has to be substituted before 4000 km is covered?

(ii) it will last more than 9000 km?

(iii) it has to be replaced after 4000 km and 14000 km is covered by it?

Solution: (i) Total number of trials = 1000.

The frequency of a tyre required to be replaced before covering 4000 km = 20

(ii) The frequency that tyre will last more than 9000 km = 325 + 445 = 770

(iii) The frequency that tyre requires replacement between 4000 km and 14000 km = 210 + 325 = 535.

So, P(E 3 ) = 535/1000 = 0.535

3. The percentage of marks obtained by a student in the monthly tests are given below:

Based on the above table, find the probability of students getting more than 70% marks in a test.

Solution: The total number of tests conducted is 5.

The number of tests when students obtained more than 70% marks = 3.

So, P(scoring more than 70% marks) = ⅗ = 0.6

Solution: Well-shuffling ensures equally likely outcomes.

(i) There are 4 aces in a deck.

Let E be the event the card drawn is ace.

The number of favourable outcomes to the event E = 4

The number of possible outcomes = 52

(ii) Let F is the event of ‘card is not an ace’

The number of favourable outcomes to F = 52 – 4 = 48

Therefore, P(F) = 48/52 = 12/13

The probability of Sangeet to win = P(S) = 0.62

The probability of Rashmi to win = P(R) = 1 – P(S)

6. Two coins (a one rupee coin and a two rupee coin) are tossed once. Find a sample space.

Solution: Either Head(H) or Tail(T) can be the outcomes.

Heads on both coins = (H,H) = HH

Head on 1st coin and Tail on the 2nd coin = (H,T) = HT

Tail on 1st coin and Head on the 2nd coin = (T,H) = TH

Tail on both coins = (T,T) = TT

Therefore, the sample space is S = {HH, HT, TH, TT}

S= {H, TH, TTH, TTTH, TTTTH,…}

Solution: S = {1, 2, 3, 4, 5, 6}, A = {2, 3, 5} and B = {1, 3, 5}

(i) A or B = A ∪ B = {1, 2, 3, 5}

(iii) A but not B = A – B = {2}

9. A coin is tossed three times, consider the following events.

Q: ‘Exactly one head appears’ and

R: ‘At Least two heads appear’.

Check whether they form a set of mutually exclusive and exhaustive events.

Solution: The sample space of the experiment is:

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} and

P ∪ Q ∪ R = {TTT, HTT, THT, TTH, HHT, HTH, THH, HHH} = S

Therefore, P, Q and R are exhaustive events.

Therefore, the events are mutually exclusive.

Hence, P, Q and R form a set of mutually exclusive and exhaustive events.

10. If P(A) = 7/13, P(B) = 9/13 and P(A∩B) = 4/13, evaluate P(A|B).

Solution: P(A|B) = P(A∩B)/P(B) = (4/13)/(9/13) = 4/9.

## Video Lesson

## Probability Important Questions

## Related Links

- Important Questions Class 9 Maths Chapter 15 Probability
- Important Questions Class 10 Maths Chapter 15 Probability
- Important Questions Class 11 Maths Chapter 16 Probability
- Important Questions Class 12 Maths Chapter 13 Probability

## Practice Questions

Solve the following probability questions.

- Write the sample space for rolling two dice.
- If two coins are tossed simultaneously, what is the probability of getting exactly two heads?
- From a well-shuffled deck of 52 cards, what is the probability of getting a king?
- In a bag, there are 5 red balls and 7 black balls. What is the probability of getting a black ball?
- If the probability of an event happening is 0.7, then what is the probability of an event that will not happen?

## Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

## Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

## Please help me solve 22; How do you set up the PMF for this...

Please help me solve 22; How do you set up the PMF for this problem, it's confusing me

## Answer & Explanation

21) Distribution of X : Binomial(5, 0.1)

21) Let X be a random variable that represents the number of sugar-addicted among 5 people.

Let's consider "finding a sugar-addicted person" as success.

Probability of success (p) = 0.10

P ( X = x ) = ( x n ) ( p ) x ( 1 − p ) n − x , x = 0 , 1 , . . . , 5

22) The mean of a binomial distribution is given by,

## Related Q&A

- Q to maximize utility. lu/courses/13/301/ Essay 2: What is Your Theory of Justice for an Entire Start Assignment Society? ... Answered over 90d ago
- Q While the law suit is going on, Rodney hires a framing crew who goes to the house and begins work. He tells them about ... Answered 27d ago
- Q Agile is more than a methodology - it's a mindset. Discuss your experience with the Agile methodology - whether professi... Answered 86d ago
- Q Discuss a Nursing Grand Rounds event encouraging technology in lifelong learning. Determine what should be included in ... Answered over 90d ago
- Q Scrolling How much time do you spend scrolling through your phone? For many (most? certainly for myself!) the answer i... Answered over 90d ago
- Q Hi, I have been struggling with this assignment. I included everything and nothing is missing, thank you very much. . ... Answered over 90d ago
- Q At 25 ∘C, the equilibrium partial pressures for the reaction A(g)+2B(g)↽−−⇀C(g)+D(g) were found to be 𝑃A=4.27 atm, 𝑃B=... Answered over 90d ago
- Q . 10.14 LAB: Book information (overriding member functions) Given main() and a base Book class, define a derived class ... Answered 28d ago
- Q Briefly describe the biological mechanism of epigenetic influences, including how they interact with our DNA and why tha... Answered 53d ago
- Q What happens to the excess demand curve when there is a positive shift in the domestic supply of a product that is being... Answered 82d ago
- Q Sales technology has given salespeople much more information and data than ever before. Using examples from the entire c... Answered over 90d ago
- Q Nestlé headquartered in Vevey, Switzerland realized its domestic market is too small. Result- today Nestlé is among the ... Answered 66d ago
- Q Tom is a Health Care Assistant in a residential care facility. One afternoon, he observes that Mrs. White seems upset. ... Answered over 90d ago
- Q Please help answer question 9- 14 9. Which of the following is one of the situations that could lead to inadequate amoun... Answered over 90d ago
- Q Write essay about Aldo store in Singapore about 1. The marquee (A marquee is a sign that displays the store's name, It c... Answered 65d ago
- Q Analyze how the Model the Way and Inspire Shared Vision practice will improve Change Management leadership areas. Analy... Answered over 90d ago
- googletag.cmd.push(function () { googletag.display('footerCliffsnotesAd'); }); CliffsNotes study guides are written by real teachers and professors, so no matter what you're studying, CliffsNotes can ease your homework headaches and help you score high on exams. About CliffsNotes

## COMMENTS

Probability of an event = (# of ways it can happen) / (total number of outcomes) P (A) = (# of ways A can happen) / (Total number of outcomes) Example 1 There are six different outcomes. What's the probability of rolling a one? What's the probability of rolling a one or a six? Using the formula from above:

Probability of "at least one" success Get 3 of 4 questions to level up! Practice Multiplication rule for dependent events Learn Dependent probability introduction Dependent probability: coins Dependent probability example Independent & dependent probability The general multiplication rule Dependent probability Practice

Finding probability is easy using the probability formula (the number of favorable outcomes divided by the total number of outcomes). In this article, we'll walk you through exactly how to use the probability formula step by step, plus show you some examples of the probability formula in action. Method 1

Exercises for Solving Probability Problems Probability Problems Solve. A number is chosen at random from 1 1 to 10 10. Find the probability of selecting a 4 4 or smaller. A number is chosen at random from 1 1 to 50 50. Find the probability of selecting multiples of 10 10. A number is chosen at random from 1 1 to 10 10.

The easiest way to solve these types of probability problems is to write out all the possible dice combinations (that's called writing a sample space ). A very simple example, if you want to know the probability of rolling a double with two die, your sample space would be: [1] [1], [1] [2], [1] [3], [1] [4], [1] [5], [1] [6],

The formula to calculate the probability of an event is equivalent to the ratio of favorable outcomes to the total number of outcomes. Probabilities always range between 0 and 1. The general probability formula can be expressed as: Probability = Number of favorable outcomes / Total number of outcomes or P (A) = f / N Where:

Answer :- A Sol: Total number of ways = 6 × 6 = 36. Probability of getting number '3′ at least one time = 1 - (Probability of getting no number 4) = 1 - (5/6) x (5/6) = 1 - 25/36 = 11/36 8. Question If a single six-sided die is rolled then find the probability of getting either 3 or 4. A) 1/2 B) 1/3 C) 1/4 D) 2/3 E) 1/6 Answer:- B Solution:-

You can solve many simple probability problems just by knowing two simple rules: The probability of any sample point can range from 0 to 1. The sum of probabilities of all sample points in a sample space is equal to 1. The probability of event A is denoted by P (A). Types 1- How to Solve Probability Questions Quickly of Random ticket or ball drawn

8th grade probability questions. 5. Alice has some red balls and some black balls in a bag. Altogether she has 25 balls. Alice picks one ball from the bag. The probability that Alice picks a red ball is x and the probability that Alice picks a black ball is 4x. Work out how many black balls are in the bag. 6 6. 100 100.

216 1 4 12 Add a comment 3 Answers Sorted by: 6 You have counted the probability that both happen twice. You have two events A is the event that a head comes up, and B is the event that a 5 or 6 comes up. The events are independent presumably, so the inclusion-exclusion formula gives: p ( A ∪ B) = p A + p B − p ( A ∩ B).

It's also known as combinations with replacement. To calculate the number of combinations with repetitions, use the following equation. Where: n = the number of options. r = the size of each combination. The exclamation mark (!) represents a factorial. In general, n! equals the product of all numbers up to n.

Question 1 A die is rolled, find the probability that an even number is obtained. Solution to Question 1 Let us first write the sample space S of the experiment. S = {1,2,3,4,5,6} Let E be the event "an even number is obtained" and write it down. E = {2,4,6} We now use the formula of the classical probability. P (E) = n (E) / n (S) = 3 / 6 = 1 / 2

Find the probability that the coin lands heads up or the number is five. Solution Let H represent heads up and T represent tails up. The sample space for this experiment is S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}. There are six ways the coin can land heads up, {H1, H2, H3, H4, H5, H6}.

Most probability questions are word problems, which require you to set up the problem and break down the information given to solve. The process to solve the problem is rarely straightforward and takes practice to perfect. Probabilities are used in mathematics and statistics and are found in everyday life, from weather forecasts to sporting events.

About this unit. How many outfits can you make from the shirts, pants, and socks in your closet? Address this question and more as you explore methods for counting how many possible outcomes there are in various situations. Learn about factorial, permutations, and combinations, and look at how to use these ideas to find probabilities.

1 Expert Answer. According to the central limit theorem the sample mean of 49 races should be approximately normally distributed with a mean of 147 with a sd of 15/sqrt (7) = 15/7 . Now you can use Z scores and the Z table to solve the rest: P (146<X<149) = P ( (146-147)/ (15/7) < Z < (149-147)/ (15/7) ) go from here/. LMK if you need more help.

In this video, Jen will show you how to solve probability questions using your understanding of independent/dependent events and algebra.THE COMPLETE UNIVERS...

Shuai Wang. 9 years ago. When A and B are independent, P (A and B) = P (A) * P (B); but when A and B are dependent, things get a little complicated, and the formula (also known as Bayes Rule) is P (A and B) = P (A | B) * P (B). The intuition here is that the probability of B being True times probability of A being True given B is True (since A ...

Probability questions and probability problems require students to work out how likely it is that something is to happen. Probabilities can be described using words or numbers. Probabilities range from 0 to 1 and can be written as fractions, decimals or percentages. ... In KS4 probability questions involve more problem solving to make ...

How to solve probability questions in a real quick ? One marble is randomly selected from a bag that contains only 4 black marbles, 3 red marbles, 5 yellow marbles, and 4 green marbles. Quantity a) The probability of selecting either a black marble or a red marble Quantity b) The probability of selecting either a yellow marble or a green marble

Probability Questions & Answers 1. Two coins are tossed 500 times, and we get: Two heads: 105 times One head: 275 times No head: 120 times Find the probability of each event to occur. Solution: Let us say the events of getting two heads, one head and no head by E 1, E 2 and E 3, respectively. P (E 1) = 105/500 = 0.21 P (E 2) = 275/500 = 0.55

Probability of success (p) = 0.10 Number of trials (n) = 5 Since number of trials are finite, each trial can result in only two mutually exclusive outcomes (success and failure), probability of success remains constant in each of the trials and outcomes in each trial are independent of others, therefore we can consider that X is following ...