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Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, is
- a)16/a2 - 6a + 10
- b)20/a2 - 6a + 10
- c)1/16
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red b...
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Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red b...
Solution:
Given,
Bag 1 contains 1 black and a2 - 6a + 9 red balls
Bag 2 contains 3 black and a2 - 6a + 7 red balls
Bag 3 contains 5 black and a2 - 6a + 5 red balls
Bag 4 contains 7 black and a2 - 6a + 3 red balls
Let A be the event of selecting a bag and B be the event of drawing a black ball.
Probability of selecting a bag, P(A) = 1/4
Let P(B/Ai) be the probability of drawing a black ball given that Ai bag is selected.
P(B/A1) = 1/10, P(B/A2) = 3/10, P(B/A3) = 5/10, P(B/A4) = 7/10
Using the law of total probability, the probability of drawing a black ball is given by,
P(B) = P(B/A1) * P(A1) + P(B/A2) * P(A2) + P(B/A3) * P(A3) + P(B/A4) * P(A4)
P(B) = (1/10) * (1/4) + (3/10) * (1/4) + (5/10) * (1/4) + (7/10) * (1/4)
P(B) = 4/10 = 2/5
The maximum value of P(B) is 2/5 which is less than 1/2. Therefore, the given answer option 'D' is correct.
Given,
Bag 1 contains 1 black and a2 - 6a + 9 red balls
Bag 2 contains 3 black and a2 - 6a + 7 red balls
Bag 3 contains 5 black and a2 - 6a + 5 red balls
Bag 4 contains 7 black and a2 - 6a + 3 red balls
Let A be the event of selecting a bag and B be the event of drawing a black ball.
Probability of selecting a bag, P(A) = 1/4
Let P(B/Ai) be the probability of drawing a black ball given that Ai bag is selected.
P(B/A1) = 1/10, P(B/A2) = 3/10, P(B/A3) = 5/10, P(B/A4) = 7/10
Using the law of total probability, the probability of drawing a black ball is given by,
P(B) = P(B/A1) * P(A1) + P(B/A2) * P(A2) + P(B/A3) * P(A3) + P(B/A4) * P(A4)
P(B) = (1/10) * (1/4) + (3/10) * (1/4) + (5/10) * (1/4) + (7/10) * (1/4)
P(B) = 4/10 = 2/5
The maximum value of P(B) is 2/5 which is less than 1/2. Therefore, the given answer option 'D' is correct.
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Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. 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 Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. 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 Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Suppose there are 4 bags. Bag 1 contains 1 black and a2 - 6a + 9 red balls, bag 2 contains 3 black and a2 - 6a + 7 red balls, bag 3 contains 5 black and a2 - 6a + 5 red balls and bag 4 contains 7 black and a2 - 6a + 3 red balls. A ball is drawn at random from a randomly chosen bag. The maximum value of probability that the selected ball is black, isa)16/a2 - 6a + 10b)20/a2 - 6a + 10c)1/16d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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