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Probability Section- 1

1.Two cards from a pack of 52 cards are lost. One card is drawn from the remaining cards. If drawn card is diamond then the probability that the lost cards were both hearts is






2. If four whole numbers taken at random are multiplied together, then the chance that the last digit in the product is 1, 3, 5, 7 is






3.Three identical dice are rolled. The probability that the same number will appear on each of them is






4.There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is






5. Two unbiased dice are thrown. The probability that neither a doublet nor a total of 10 will appear is






6.Two dice are thrown the events A, B, C are as follows A: Getting an odd number on the first die. B: Getting a total of 7 on the two dice. C: Getting a total of greater than or equal to 8 on the two dice. Then AUB is equal to






7. Two numbers are chosen from {1, 2, 3, 4, 5, 6} one after another without replacement. Find the probability that the smaller of the two is less than 4.






8.The probability that when a hand of 7 cards is drawn from a well-shuffled deck of 52 cards, it contains 3 Kings is






9.The probability that in a random arrangement of the letters of the word INSTITUTION the three T are together is






10.Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is






11. A bag contains 5 brown and 4 white socks . A man pulls out two socks. The probability that both the socks are of the same colour is






12. When a coin is tossed 8 times getting a head is a success. Then the probability that at least 2 heads will occur is






13. A couple has two children. The probability that both children are females if it is known that the elder child is a female is






14.Let A and B are two mutually exclusive events and if P(A) = 0.5 and P(B ̅) = 0.6 then P(A∪B) is






15. The probability of getting 53 Sundays in a leap year is






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