Given two independent events, if the probability that both the events occur is 8 49 , the probability that exactly one of them occurs is 26 49 and the probability of more probable of the two events is λ , then 14 λ is equal to

Step-by-step solution

Let, A and B are two independent events P A ∩ B = P A ⋅ P B = 8 49 … 1 P A ∩ B c + P B ∩ A c = 26 49 ⇒ P A + P B - 2 P A ⋅ P B = 26 49 ⇒ P A + P B = 42 49 = 6 7 … 2 From 1 and 2 , we get, P A = 4 7 , P B = 2 7 or P A = 2 7 , P B = 4 7 hence, the probability of the more probable event is λ = 4 7