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. A certain company sells tractors which fail at a rate of 1 out of 1000. If 500 tractors are purchased from this company, what is the probability of 2 of them failing within first year

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