Quant Exam > Quant Questions > A suitcase contains 4 blue shirts, 5 red shir...
Start Learning for Free
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?
- a)113/218
- b)14/167
- c)123/234
- d)224/495
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If ...
P = 4C1*8C3/12C4 = 4*56/495 = 224/495
Most Upvoted Answer
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If ...
Question category: Quant
Given:
A suitcase contains 4 blue shirts, 5 red shirts, and 3 white shirts.
4 shirts are drawn.
To find:
The probability that exactly one of them is blue.
Solution:
Total number of shirts in the suitcase = 4 + 5 + 3 = 12
Total number of ways to draw 4 shirts out of 12 = 12C4 (combination of 4 shirts out of 12)
Number of ways to draw exactly one blue shirt and three other shirts (not blue) = 4C1 * 8C3 (combination of 1 blue shirt out of 4 and 3 shirts out of 8 which are not blue)
Therefore, the required probability = (4C1 * 8C3) / 12C4
= (4*56) / 495
= 224/495
Hence, option D is the correct answer.
Note: The formula used here is the formula for probability of an event happening exactly k times in n independent trials, which is given by nCk * p^k * (1-p)^(n-k), where p is the probability of the event happening in one trial. In this case, p = 4/12 = 1/3 (the probability of drawing a blue shirt in one trial), n = 4 (the number of trials), and k = 1 (the number of times we want the event to happen). So, the required probability is 4C1 * (1/3)^1 * (2/3)^3 = 4/9 * 8/27 = 32/81. However, this is not one of the given options, so we need to simplify our answer.
Given:
A suitcase contains 4 blue shirts, 5 red shirts, and 3 white shirts.
4 shirts are drawn.
To find:
The probability that exactly one of them is blue.
Solution:
Total number of shirts in the suitcase = 4 + 5 + 3 = 12
Total number of ways to draw 4 shirts out of 12 = 12C4 (combination of 4 shirts out of 12)
Number of ways to draw exactly one blue shirt and three other shirts (not blue) = 4C1 * 8C3 (combination of 1 blue shirt out of 4 and 3 shirts out of 8 which are not blue)
Therefore, the required probability = (4C1 * 8C3) / 12C4
= (4*56) / 495
= 224/495
Hence, option D is the correct answer.
Note: The formula used here is the formula for probability of an event happening exactly k times in n independent trials, which is given by nCk * p^k * (1-p)^(n-k), where p is the probability of the event happening in one trial. In this case, p = 4/12 = 1/3 (the probability of drawing a blue shirt in one trial), n = 4 (the number of trials), and k = 1 (the number of times we want the event to happen). So, the required probability is 4C1 * (1/3)^1 * (2/3)^3 = 4/9 * 8/27 = 32/81. However, this is not one of the given options, so we need to simplify our answer.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A suitcase contains 4 blue shirts, 5 red shirts and 3 white shirts.If 4 shirts are drawn what is the probability that exactly one of them is blue ?a)113/218b)14/167c)123/234d)224/495e)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup