Let A and B are two independent events. If the probability that both A and B occur together is 1 6 and the probability that neither of them occurs is 1 3 , then the probability of occurrence of A is

Step-by-step solution

P A ∩ B = 1 6 and P A C ∩ B C = 1 3 Now, P A ∪ B C = P A C ∩ B C = 1 3 ⇒ 1 - P A ∪ B = 1 3 ⇒ P A ∪ B = 2 3 But P A ∪ B = P A + P B - P A ∩ B ⇒ P A + P B = 5 6       . . . i ∵   A and B are independent events ∴   P A ∩ B = P A P B ⇒ P A P B = 1 6 P A - P B 2 = P A + P B 2 - 4 P A P B = 25 36 - 4 6 = 1 36 ⇒ P A - P B = ± 1 6         . . . ii On solving Eqs. (i) and (ii), we