Question 3:

(a) A card is drawn at random from an ordinary deck of 52 playing cards. Find the probability that the card is (i) a jack (ii) not a jack.

(b) Two dice are rolled once. What is the probability of getting a total of7 or 11.

(c) A class contains 16 boys and 10 girls of which half of the girls are fat. Find the probability that a student chosen at random is a boy or a fat student.

(d) A die is tossed only once. What is the probability that either a number less than 5 or an even number occurs on the die.

(e) A bag contains 5 red and 7 black balls. A ball is drawn at random from the bag, the color is noted and the ball is replaced. A second ball is then drawn. Find the probability that the first ball is red and the second is black.

(f) A box contains 8 tickets bearing the numbers 1,2,3,4,5,6,8,10.One ticket is drawn and kept aside. Then a second ticket is drawn. What is the probability that both the tickets show even numbers.

(g) The probability that a contractor gets an electric contract is 2/7 and that of his getting a plumbing contract is 3/5.If the probability of his getting at least one of the contracts is 5/7.What is the probability of his getting both the contracts.

(h) A card is taken from a well shuffled pack of cards. Then a second card is drawn. Find the probability that both are spades in case the first card is (i) is replaced (ii) is not replaced.

(i) Suppose that we have a fuse box containing 40 fuses of which 6 are defective. If two fuses are selected at random and removed from the box. Find the probability that they both are defective, if the first fuse

i)Replacedii) Not replaced

(j) In how many ways can 5 people line up for a photograph.

(k) There are 3 white, 2 red and 4 green flags.In how many ways it can be arranged in a row.

(l) A batch contains 6 boys and 4 girls. A group of 4 student is selected. How many groups may be formed of exactly 2 girls.

(m) Find the permutation of the word COMMISSIONER.

(n) In how many ways 4person can be selected from 8 men and 6 women when there is equal representation for both.

(o) In how many ways 8 persons can be seated around a circular table