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A bag ‘A’ contains 2 white and 3 red balls and a bag ‘B’ contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:
- a)27/52
- b)3/5
- c)25/52
- d)5/9
Correct answer is option 'C'. Can you explain this answer?
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A bag A contains 2 white and 3 red balls and a bag B contains 4 white ...
If we assume that it is equally likely that the ball is drawn from either bag, then we proceed as follows. Let R be the event that a red ball is drawn, and let B be the event that bag B is chosen for the drawing. Then
P(B) = P(not B) = 1/2
P(R|B) = 5/9 = P(RB) / P(B) = 2 P(RB),
P(R|not B) = 3/5 = P(R not B) / P(not B) = 2 P(R not B)
P(R) = P(RB) + P(R not B) = (1/2)( 5/9 + 3/5 ) = 26/45
P(B|R) = P(RB) / P(R) = (5/9)(1/2) / (26/45) = 25/52
P(B) = P(not B) = 1/2
P(R|B) = 5/9 = P(RB) / P(B) = 2 P(RB),
P(R|not B) = 3/5 = P(R not B) / P(not B) = 2 P(R not B)
P(R) = P(RB) + P(R not B) = (1/2)( 5/9 + 3/5 ) = 26/45
P(B|R) = P(RB) / P(R) = (5/9)(1/2) / (26/45) = 25/52
Most Upvoted Answer
A bag A contains 2 white and 3 red balls and a bag B contains 4 white ...
Probability of drawing a red ball from each bag:
- Bag A: P(red|A) = 3/5
- Bag B: P(red|B) = 5/9
Probability of drawing a red ball from any bag:
- P(red) = P(red from A) * P(A) + P(red from B) * P(B)
- P(red) = (3/5 * 1/2) + (5/9 * 1/2) = 27/45 = 3/5
Probability that the red ball was drawn from bag B:
- P(B|red) = P(red from B) * P(B) / P(red)
- P(B|red) = (5/9 * 1/2) / (3/5) = 5/18 / 3/5 = 25/54 = 25/52
Therefore, the probability that the red ball was drawn from bag B is 25/52.
- Bag A: P(red|A) = 3/5
- Bag B: P(red|B) = 5/9
Probability of drawing a red ball from any bag:
- P(red) = P(red from A) * P(A) + P(red from B) * P(B)
- P(red) = (3/5 * 1/2) + (5/9 * 1/2) = 27/45 = 3/5
Probability that the red ball was drawn from bag B:
- P(B|red) = P(red from B) * P(B) / P(red)
- P(B|red) = (5/9 * 1/2) / (3/5) = 5/18 / 3/5 = 25/54 = 25/52
Therefore, the probability that the red ball was drawn from bag B is 25/52.
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A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:a)27/52b)3/5c)25/52d)5/9Correct answer is option 'C'. Can you explain this answer?
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A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:a)27/52b)3/5c)25/52d)5/9Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:a)27/52b)3/5c)25/52d)5/9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:a)27/52b)3/5c)25/52d)5/9Correct answer is option 'C'. Can you explain this answer?.
A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:a)27/52b)3/5c)25/52d)5/9Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:a)27/52b)3/5c)25/52d)5/9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is:a)27/52b)3/5c)25/52d)5/9Correct answer is option 'C'. Can you explain this answer?.
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