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Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?
- a)20/63
- b)35/71
- c)43/63
- d)36/71
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two boxes A and B contain white and black balls. Box A contains 4 bla...
Probability of choosing either of the boxes = ½
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The probability of drawing a white ball from box A = 1/2 x 5/9 = 5/18
The probability of drawing a white ball from box B = 1/2 × 4/7 = 2/7
The probability of drawing a white ball = 5/18 + 2/7 = 35+36/126 = 71/126
It is given that the ball drawn was white.
Hence the probability that the white ball was drawn from box A = 5/18/71/126 = 35/71
Most Upvoted Answer
Two boxes A and B contain white and black balls. Box A contains 4 bla...
To find the probability of drawing a white ball from box A, we need to use Bayes' theorem. Bayes' theorem states that the probability of an event A occurring given that event B has occurred is equal to the probability of event B occurring given that event A has occurred, multiplied by the probability of event A occurring, divided by the probability of event B occurring.
Let's denote the events as follows:
A: Drawing a white ball from box A
B: Drawing a white ball
We are given the following information:
P(A) = probability of drawing a white ball from box A = 5/9
P(B|A) = probability of drawing a white ball given that it is from box A = 5/9
P(B) = probability of drawing a white ball = ?
To find P(B), we need to consider the probabilities of drawing a white ball from both boxes.
P(B) = P(B|A) * P(A) + P(B|B) * P(B)
P(B|B) = probability of drawing a white ball given that it is from box B = 4/7
P(B|A) = probability of drawing a white ball given that it is from box A = 5/9
Now we can substitute the values into the equation:
P(B) = (5/9) * (5/9) + (4/7) * (4/9)
= 25/81 + 16/63
= (25 * 7 + 16 * 9) / (81 * 7)
= (175 + 144) / 567
= 319 / 567
Simplifying the fraction, we get:
P(B) = 319 / 567 = 35/71
Therefore, the probability of drawing a white ball from box A, given that it is a white ball, is 35/71.
Let's denote the events as follows:
A: Drawing a white ball from box A
B: Drawing a white ball
We are given the following information:
P(A) = probability of drawing a white ball from box A = 5/9
P(B|A) = probability of drawing a white ball given that it is from box A = 5/9
P(B) = probability of drawing a white ball = ?
To find P(B), we need to consider the probabilities of drawing a white ball from both boxes.
P(B) = P(B|A) * P(A) + P(B|B) * P(B)
P(B|B) = probability of drawing a white ball given that it is from box B = 4/7
P(B|A) = probability of drawing a white ball given that it is from box A = 5/9
Now we can substitute the values into the equation:
P(B) = (5/9) * (5/9) + (4/7) * (4/9)
= 25/81 + 16/63
= (25 * 7 + 16 * 9) / (81 * 7)
= (175 + 144) / 567
= 319 / 567
Simplifying the fraction, we get:
P(B) = 319 / 567 = 35/71
Therefore, the probability of drawing a white ball from box A, given that it is a white ball, is 35/71.
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Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?a)20/63b)35/71c)43/63d)36/71e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?a)20/63b)35/71c)43/63d)36/71e)None of theseCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?a)20/63b)35/71c)43/63d)36/71e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?a)20/63b)35/71c)43/63d)36/71e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?a)20/63b)35/71c)43/63d)36/71e)None of theseCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?a)20/63b)35/71c)43/63d)36/71e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two boxes A and B contain white and black balls. Box A contains 4 black and 5 white balls, while box B contains 3 black and 4 white balls. One of the balls is randomly drawn from one of the two boxes. Find the probability of the ball being drawn from box A if it is known that it is a white ball?a)20/63b)35/71c)43/63d)36/71e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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