UPSC Exam > UPSC Questions > A committee of 7 members is to be formed by s...
Start Learning for Free
A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.?
Most Upvoted Answer
A committee of 7 members is to be formed by selecting numbers at rando...
Probability of Forming a Committee with at least 3 Women and at most 6 Men
1. Total Number of Ways to Form a Committee
- Total candidates = 14 (5 women and 9 men)
- Total ways to form a committee of 7 members = C(14, 7)
2. Number of Ways to Form a Committee with at least 3 Women
- Number of ways to select 3 women out of 5 = C(5, 3)
- Number of ways to select remaining 4 members from the pool of 9 men = C(9, 4)
- Total ways to form a committee with at least 3 women = C(5, 3) * C(9, 4)
3. Number of Ways to Form a Committee with at most 6 Men
- Number of ways to select 0 men out of 9 = C(9, 0)
- Number of ways to select remaining 7 members from the pool of 5 women = C(5, 7)
- Total ways to form a committee with at most 6 men = C(9, 0) * C(5, 7) + C(9, 1) * C(5, 6) + ... + C(9, 6) * C(5, 1) + C(9, 7) * C(5, 0)
4. Calculating the Probability
- Probability of forming a committee with at least 3 women = Number of ways to form a committee with at least 3 women / Total number of ways to form a committee
- Probability of forming a committee with at most 6 men = Number of ways to form a committee with at most 6 men / Total number of ways to form a committee
5. Final Steps
- Calculate the probabilities using the formulas derived in steps 2 and 3
- Simplify the expressions to get the final probability values.
1. Total Number of Ways to Form a Committee
- Total candidates = 14 (5 women and 9 men)
- Total ways to form a committee of 7 members = C(14, 7)
2. Number of Ways to Form a Committee with at least 3 Women
- Number of ways to select 3 women out of 5 = C(5, 3)
- Number of ways to select remaining 4 members from the pool of 9 men = C(9, 4)
- Total ways to form a committee with at least 3 women = C(5, 3) * C(9, 4)
3. Number of Ways to Form a Committee with at most 6 Men
- Number of ways to select 0 men out of 9 = C(9, 0)
- Number of ways to select remaining 7 members from the pool of 5 women = C(5, 7)
- Total ways to form a committee with at most 6 men = C(9, 0) * C(5, 7) + C(9, 1) * C(5, 6) + ... + C(9, 6) * C(5, 1) + C(9, 7) * C(5, 0)
4. Calculating the Probability
- Probability of forming a committee with at least 3 women = Number of ways to form a committee with at least 3 women / Total number of ways to form a committee
- Probability of forming a committee with at most 6 men = Number of ways to form a committee with at most 6 men / Total number of ways to form a committee
5. Final Steps
- Calculate the probabilities using the formulas derived in steps 2 and 3
- Simplify the expressions to get the final probability values.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.?
Question Description
A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.?.
A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.?.
Solutions for A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? defined & explained in the simplest way possible. Besides giving the explanation of
A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.?, a detailed solution for A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? has been provided alongside types of A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? theory, EduRev gives you an
ample number of questions to practice A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee b) At most 6 men in the committee.? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup