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If from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is
- a)13/32
- b)12/14
- c)12/25
- d)3/13
Correct answer is option 'A'. Can you explain this answer?
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If from each of three boxes containing 3 white and 1 black, 2 white an...
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If from each of three boxes containing 3 white and 1 black, 2 white an...
Solution:
Given,
Box 1 contains 3 white and 1 black ball
Box 2 contains 2 white and 2 black ball
Box 3 contains 1 white and 3 black ball
Let's calculate the probability of drawing 2 white and 1 black ball separately from each box.
Probability from Box 1:
The probability of drawing 2 white balls and 1 black ball from Box 1 can be calculated as follows:
Probability of drawing the first white ball = 3/4
Probability of drawing the second white ball = 2/3
Probability of drawing the black ball = 1/2
Therefore, the probability of drawing 2 white balls and 1 black ball from Box 1 = (3/4) x (2/3) x (1/2) = 1/4
Probability from Box 2:
The probability of drawing 2 white balls and 1 black ball from Box 2 can be calculated as follows:
Probability of drawing the first white ball = 2/4
Probability of drawing the second white ball = 1/3
Probability of drawing the black ball = 2/2
Therefore, the probability of drawing 2 white balls and 1 black ball from Box 2 = (2/4) x (1/3) x 1 = 1/6
Probability from Box 3:
The probability of drawing 2 white balls and 1 black ball from Box 3 can be calculated as follows:
Probability of drawing the first white ball = 1/4
Probability of drawing the black ball = 3/3
Probability of drawing the second white ball = 0/2 (as there are no white balls left in the box)
Therefore, the probability of drawing 2 white balls and 1 black ball from Box 3 = 0
Total probability:
Now, we need to add up the probabilities from all three boxes to get the total probability of drawing 2 white balls and 1 black ball.
Total probability = Probability from Box 1 + Probability from Box 2 + Probability from Box 3
Total probability = 1/4 + 1/6 + 0
Total probability = 13/24
Therefore, the probability of drawing 2 white balls and 1 black ball is 13/24, which is closest to option A (13/32).
Given,
Box 1 contains 3 white and 1 black ball
Box 2 contains 2 white and 2 black ball
Box 3 contains 1 white and 3 black ball
Let's calculate the probability of drawing 2 white and 1 black ball separately from each box.
Probability from Box 1:
The probability of drawing 2 white balls and 1 black ball from Box 1 can be calculated as follows:
Probability of drawing the first white ball = 3/4
Probability of drawing the second white ball = 2/3
Probability of drawing the black ball = 1/2
Therefore, the probability of drawing 2 white balls and 1 black ball from Box 1 = (3/4) x (2/3) x (1/2) = 1/4
Probability from Box 2:
The probability of drawing 2 white balls and 1 black ball from Box 2 can be calculated as follows:
Probability of drawing the first white ball = 2/4
Probability of drawing the second white ball = 1/3
Probability of drawing the black ball = 2/2
Therefore, the probability of drawing 2 white balls and 1 black ball from Box 2 = (2/4) x (1/3) x 1 = 1/6
Probability from Box 3:
The probability of drawing 2 white balls and 1 black ball from Box 3 can be calculated as follows:
Probability of drawing the first white ball = 1/4
Probability of drawing the black ball = 3/3
Probability of drawing the second white ball = 0/2 (as there are no white balls left in the box)
Therefore, the probability of drawing 2 white balls and 1 black ball from Box 3 = 0
Total probability:
Now, we need to add up the probabilities from all three boxes to get the total probability of drawing 2 white balls and 1 black ball.
Total probability = Probability from Box 1 + Probability from Box 2 + Probability from Box 3
Total probability = 1/4 + 1/6 + 0
Total probability = 13/24
Therefore, the probability of drawing 2 white balls and 1 black ball is 13/24, which is closest to option A (13/32).
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Question Description
If from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn isa)13/32b)12/14c)12/25d)3/13Correct answer is option 'A'. 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 If from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn isa)13/32b)12/14c)12/25d)3/13Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn isa)13/32b)12/14c)12/25d)3/13Correct answer is option 'A'. Can you explain this answer?.
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