Given two independent events, if the probability that exactly one of them occurs is 26 49 and the probability that none of them occurs is 15 49 , then the probability of more probable of the two events is :

Step-by-step solution

Let the probability of occurrence of first event A, be ' a ' i..e., P ( A )= a P ( not A )=1-a And also suppose that probability of occurrence of second event B , P ( B )=b , P ( not B )=1-b Now, P ( A and not B )+ P ( not A and B )= 26 49 aligned & P ( A ) P ( not B )+ P ( not A ) P ( B )= 26 49 & a (1-b)+(1-a) b= 26 49 & a+b-2 a b= 26 49 aligned And P ( not A and not B )= 15 49 aligned & P ( not A ) P ( not B )= 15 49 & (1-a) (1-b)= 15 49 & 1- b - a + ab = 15 49 & a+b-a b= 34 49 aligned From (i) and (ii), a+b= 42