Probability

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #121

There are three bags each containing 5 red and 5 black balls. One ball is transferred blindly from the first to the second bag and then one ball is transferred blindly from the second to the third. A ball is now drawn from the third bag. Find the probability that the drawn ball is red.
Ans: `1/2`
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Question No: #122

There are two bags. Bag I contains 5 red & 4 black balls, bag II contains 3 red & 5 black balls. One bag is chosen at random and one ball is drawn from it. What is the probability that the ball is red?
Ans: `67/144`
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Question No: #123

There are 3 identical urns. First urn contains 3 white and 2 red balls, second urn contains 7 white and 3 red balls and third urn contains 5 white and 3 red balls. Probability of choosing any urn is same. An urn is selected at random and a ball is drawn from it. What is the probability that the ball is white?
Ans: `77/120`
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Question No: #124

There are 3 white & 2 red balls in a bag. One ball is drawn. Then another ball is drawn without replacing the first ball. Then the probability of 2nd ball is red is -
(a) `8/25`, (b) `2/5` (c) `3/5`, (d) `21/25`
Ans: (b) `2/5`
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Question No: #125

A bag contains 3 red & 7 black balls. Two balls are drawn randomly one by one without replacement. If second ball drawn is red color, then find the probability of first ball drawn is also red.
Ans: `1/15`
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Question No: #126

A bag contains 4 white & 6 black balls. Two balls are drawn randomly one by one without replacement. If first ball drawn is white color, then find the probability of second ball drawn is also white.
Ans: `2/15`
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Question No: #127

There are two bags. Bag I contains 4 red & 4 black balls, bag II contains 2 red & 6 black balls. One bag is chosen at random and a ball is drawn from it and it is found as a red ball. What is the probability that it is drawn from first bag?
Ans: `2/3`
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Question No: #128

There are three bags. Bag A contains 6 red & 4 white balls; bag B contains 2 red & 6 white balls; bag C contains 1 red & 5 white balls. One bag is chosen at random and a ball is drawn from it and it is found as a red ball. What is the probability that the ball is drawn from bag A?
Ans: `36/61`
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Question No: #129

There are three bags. Bag A contains 2 white, 1 black & 3 red balls; bag B contains 3 white, 2 black & 4 red balls; bag C contains 4 white, 3 black & 2 red balls. One bag is chosen randomly and 2 balls are drawn from it. If the balls drawn are 1 black & 1 red, then find the probability that they are drawn from bag B.
Ans: `20/53`
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Question No: #130

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?
Ans: `4/9`
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