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# Important Questions of Probability & Statistics for GATE Examination

## Important Questions of Probability & Statistics for GATE Examination

### Probability and Statistics GATE Questions

Q. What is the chance that a leap year will have 53 Sundays?
Solution-

Q. What is the chance that a non-leap year will have 53 Sundays?
Solution-

Q. A card is drawn from a deck of a playing card, what is the probability that it is a face card?

Q. A card is drawn from a deck of a playing card, what is the probability that it is a heart card?

Q. A card is drawn from a deck of a playing card, what is the probability that it is a face and heart card?

Q. A card is drawn from a deck of a playing card, what is the probability that it is a face or heart card?

Q. From a deck of a playing card, two cards are drawn at random. What is the probability that both cards will be king? If the first card is not replaced.

Q. From a deck of a playing card, two cards are drawn at random. What is the probability that both cards will be king? If the replacement is allowed.

Q. A bag contains 3 red, 6 white and 7 black balls. What is the probability that two balls drawn are white and black?

Q. A problem in mathematics is given to three students A, B and C, whose chances of solving are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

Q.  An integer is selected at random from first 200 digits. What is the probability that the integer is chosen is divisible by either 6 or 8.

Q. 'A' hits a target 4 times in 5 shots. 'B' hits a target 3 times in 4 shots. 'C' hits a target 2 time in 3 shots. They fire a volley. What is the probability that 2 shot at least hit?

Q. The probability of 'A' hit a target is 1/4, 'B' hit a target is 2/5. Both shot at the target. Find the probability that at least one of them hits the target.

Q. A husband and a wife appear in an interview for two vacant seats in the same post. The probability of husband selection is 1/7 and that of wife selection is 1/5. What is the probability that-
(i) Both of them are selected
(ii) Only one of them is selected
(iii) None of them is selected

Q. In a certain college, 25% of students are failed in Math and 15% fails in Chemistry. and 10% failed in both Math and Chemistry. If a student is selected at random.
(i) If he failed in chemistry then what is the probability that- he failed in Mathematics.
(ii) If he failed in Mathematics then what is the probability that- he failed in Chemistry.
(iii) What is the probability that he failed neither Math nor Chemistry?

Q. In a particular bank, 60% of all customers applied for a loan are rejected. If 4 new loan applications are received find the probability that 3 of them are accepted?

Q. A pair of dice is thrown, If the two number appears are different. Find the probability that-
(i) the sum is 6
(ii) an ace appears
(iii) the sum is 4 or less.

Q.  Team 'A' has a 2/3 probability of winning when it plays. Suppose 'A' plays 4 games, Find the probability that A wins more than 1/2 of its game.

Q. A player tosses two fair coins. He wins 2 dollars if 2 Head occur and 1 dollar if 1 head occur. On the other hand, he looses 3 dollars if no head occur. Find the expected value E of the game.

Q. Five fair coins are tossed simultaneously. Find the probability that at least one head turned up.

Q. Four fair coins are tossed simultaneously. Find the probability that at least one head and one tail turned up.

Q. There are 5 duplicate and 10 original items in an automobile shop. Three items are bought at random by a customer. Find the probability that none of the items is duplicate.

Q.

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