Let S be a set of 5 elements and P ( S ) denote the power set of S. Let E be an event of choosing an ordered pair ( A , B ) from the set P ( S ) P ( S ) such that A B = . If the probability of the event E is 3^ p 2^ q , where p, q N , then p+q is equal to _ _ _ _

Step-by-step solution

S has 5 elements, so P(S) has 2^5 = 32 subsets. Total ordered pairs from P(S) P(S) is 32^2 = 1024 For pairs (A, B) with A B = : each of the 5 elements has 3 choices - in A only, in B only, or in neither Number of favorable outcomes = 3^5 = 243 Probability = 243 1024 = 3^5 2¹⁰ With p = 5 and q = 10 , we get p + q = 15