Question

A bag contains 10 tickets numbered 0, 1,2 ....9. Two tickets are drawn at random simultaneously. What is probability that (a) product of the numbers on the two tickets drawn is (b) sum of the numbers on the two tickets ¡s less than 4 (c) One ticket number is 3 times the other ticket number. Select the correct answer from above options

Answer 1

Let n(S)= 10C2 = 10 × 9 2 × 1 = 45 (a) Let A: Product of the members is 0 = {(0. 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9)} n(A) = 9 (b) Let B: sum is less than 4 B = {(0, 1) (0, 2) (0, 3) (1, 2)} n(B) = 4 (c) Let C: one number is 3 times the other C = ((1,3) (2,6)(3,9)} ⇒ n(C) = 3