1. In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded.
What is the probability of not getting a prize if you buy
(a) one ticket
(b) two tickets
(c) 10 tickets.

2. Out of 100 students, two sections of 40 and 60 are formed. If you and your friend
are among the 100 students, what is the probability that
(a) you both enter the same section?
(b) you both enter the different sections?

3. Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its
proper envelope.

4. If E and F are events such that P(E) =1/4, P(F) =1/2 and P(E and F) =1/8,find
(i) P(E or F),
(ii) P(not E and not F).

5. Events E and F are such that P(not E or not F) = 0.25, State whether E and F are
mutually exclusive.

6. A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35.
Find (i) P(A ∪ B) (ii) P(A´ ∩ B´) (iii) P(A ∩ B´) (iv) P(B ∩ A´)

7. If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when,
(i) the digits are repeated?
(ii) the repetition of digits is not allowed?

8. The number lock of a suitcase has 4 wheels, each labeled with ten digits i.e., from 0 to

9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase?

9. Two balls are drawn at random with replacement from a box containing 10 black
and 8 red balls. Find the probability that
(i) both balls are red.
            (ii) first ball is black and second is red.
(iii) one of them is black and other is red.

10. An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

11.Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on  consecutive days?

12. In answering a question on a multiple choice test, a student either knows the answer or guesses. Let 3/4 be the probability that he knows the answer and ¼ be the probability that he guesses. Assuming that a student who guesses at theanswer will be correct with probability 1/4 . What is the probability that the student knows the answer given that he answered it correctly?

13.A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.