Probability

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

Click on each question to see answer & solution.

Question No: #131

There are 3 coins in a box. The probability of getting head is `2/3` for two of them, while for remaining it is `1/2`. A coin is chosen at random and tossed 3 times, showing head in each case. What is the probability that the coin is unbiased ?
Ans: `27/155`
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Question No: #132

A and B toss a coin alternately till one of them tosses a head and wins the game. If A starts the game, what are their respective probability of winning?
Ans: Probability of A Winning the game is `2/3` and B Winning the game is `1/3`
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Question No: #133

Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head ?
Ans: `1/3`
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Question No: #134

Suppose 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
Ans: `20/21`
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Question No: #135

Out of 20 games of chess played between two players A and B, A won 12, B won 4 and 4 ended in a tie. In a tournament of three games find the probability that (i) B wins at least one game, (ii) two games end in a tie.
Ans: (i) `61/125`, (ii) `12/125`
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Question No: #136

A machine operates only when all of its three components function. The probabilities of the failures of the first , second and third component are 0.2, 0,3 and 0.5 respectively . What is the probability that the machine will fail ?
Ans: `0.72`
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Question No: #137

There are 30 boys and 20 girls in a class. Half of the boys and half of the girls are of blue eyes. If one candidate is selected at random from the class, find the probability that it is either a boy or a blue eyed.
Ans: `4/5`
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Question No: #138

An insurance company insured 2000 scooters and 3000 motor cycles. The probability of an accident involving a scooter is 0.01 and that of a motor cycle is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motor cycle.
Ans: `3/4`
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Question No: #139

In a factory there are three types of Machines `M_1, M_2, M_3` which produces 2000, 2500 and 4000 bolts daily respectively. `M_1, M_2, M_3` produces 3%, 4% and 2.5% defective products respectively. A bolt is drawn at random from the product and is found to be defective. What is the probability of that it is manufactured by machine `M_2`?
Ans: `5/13`
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Question No: #140

In a bulb factory, machines A, B and C manufacture 60%, 30% and 10% bulbs respectively. 1%, 2% and 3% of the bulbs produced respectively by machines A, B and C are found to be defective. A bulb is picked up at random from the total production and found to be defective. Find the probability that this bulb was produced by the machine A.
Ans: `2/5`
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