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**Important Questions of Probability & Statistics for GATE Examination**

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**Probability and Statistics GATE Questions**

**Q.**

**What is the chance that a leap year will have 53 Sundays**

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**Solution-**

**Q.**

**What is the chance that a non-leap year will have 53 Sundays**

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**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.**

**More Questions will be updated soon...**

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