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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

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

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

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

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

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

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

7.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.

8.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.

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

10.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?

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

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

13.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.

14.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

15.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?

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

17.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.

18.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.

19.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 loses 3 dollars if no head occurs. Find the expected value E of the game.

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

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

22.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.

23.Q. A book of 300 pages contains 30 printing mistakes. Assumes that these errors are randomly distributed throughout the book and X is the number of errors per page has a Poisson's distribution. What is the probability that 20 pages selected at random will be free of errors?

24.Q. A single dice is thrown twice, What is the probability that their sum is neither 8 nor 9?

25.Q. Find the probability that almost 5 defective fuses will be formed in a box of 200 fuses. If experience shows that 2% of such fuses are defective.

26.Q.  A lot has 10% defective items are chosen randomly from this lot. What is the probability that exactly two of the chosen items are defective?

27.Q. Two bags contain 10 coins each and coins in each bag are numbered from 1 to 10. One coin is drawn at random from each bag. What is the probability that one of the coins has the value (1,2,3 or 4) while the other has (7,8,9 or 10)?

28.Q. A box contains 20 defectives and 80 non-defective items. If two items are selected at random without replacement, What will be the probability that both items are defective?

29.Q. A box contains 3 blue balls and 4 red balls. Another identical box contains 2 blue balls and 5 red balls. One ball is picked at random from one of the two boxes and it is red. The probability that it came from the first box is?

30.Q. A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box without replacement of the first ball. The probability for both the balls being red is?

31.Q. Box P has 2 red and 3 blue balls and box Q has 3 Red and 1 blue ball. The probability of selecting boxes P and Q are 1/3 and 2/3 respectively. A ball is selected from one of the two boxes and it is red then what is the probability that it comes from box P?

(Last Updated 22-04-2021)

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