Question

Two dice are rolled find the probability of the sum of both faces is a prime number ,the sum divisible by 7 and 11 ,,product of both faces is divisible by 4,first face is a prime number and second is divisible by 3

Answer 1

Clearly, we have
A = {(1, 1)}, B = {(1, 2), (2, 1)} and C = {(1, 3), (3, 1), (2, 2)}.

(i) Since A consists of a single sample point, it is a simple event.

(ii) Since both B and C contain more than one sample point, each one of them is a compound event.

(iii) Since A ∩ B = ∅, A and B are mutually exclusive.

Answer 2

(3,3),(3,5),(5,3),(5,5). i.e,1/9
(1,6),(2,5),(3,4),(4,3),(5,2),(6,1). i.e,1/6
2/36. i.e,1/18
6/36. i.e,1/6