Probability

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

Click on each question to see answer & solution.

Question No: #101

`A` speaks lie 3 times out of 4 times. A die is tossed and he reports that it was 6. What is the probability that It was actually 6?
Ans: `3/8`
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Question No: #102

A bag contains 6 balls of different colours and a ball is drawn from it. A's probability of speaking the truth is `\frac{2}{3}` and B's probability of speaking thetruth is `\frac{4}{5}`. If both A and B say that a red ball has been drawn, then find the probability that actually a red ball has been drawn.
Ans: `40/41`
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Question No: #103

Probability of solving a specific problem independently by three students are `1/2, 1/3` & `1/4`. If all are trying to solve the problem independently then find the probability that
i) the problem is solved, ii) exactly one of them solves the problem, iii) exactly two of them solve the problem.
Ans: i) `1/2` , ii) `11/24`, iii) `6\log_3e`
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Question No: #104

If on an average 1 vessel in every 10 is wrecked, find the chance that out of 5 vessels expected 4 at least will arrive safely.
Ans: `\frac{45927}{50000}`
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Question No: #105

One Number is chosen at random from the integers 1 to 50. What is the probability that it is divisible by 4 or 6?
Ans: `8/25`
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Question No: #106

One Number is chosen at random from the integers 1 to 50. What is the probability that it is divisible by 4 or 5?
Ans: `2/5`
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Question No: #107

The odds against two events are `2:7` and `7:5` respectively. If the events are independent, then find the probability that at least one will occur.
Ans: `47/54`
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Question No: #108

The odds against a man who is 45 years old living till he is 70 are 7:5 and the odds against his wife who is now 36 living till she is 61 are 5:3 Find the probability that
(i) The couple will be alive 25 years hence,
(ii) At least one of them will be alive 25 years hence.
Ans: (i) `5/32`, (ii) `61/96`
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Question No: #109

A bag contains 4 balls.Two balls drawn at random without replacement and are found to be white. What is the probability that all balls are white?
Ans: `3/5`
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Question No: #110

There are 2 white, 3 red & 4 black balls. One ball is drawn from the bag and then again one ball is drawn from the bag. What is the probability of at least one red ball among 2 drawn balls?
Ans: `7/12`
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