Let A and B be two independent events of a random experiment. If the probability that both A and B occur is 1 6 and the probability that neither of them occur is 1 3 , then the probability of occurrence of A is

Step-by-step solution

Since A & B are independent events so P ( A B )= P ( A ) P ( B ) Now, P ( A B )= 1 6 P ( A ) P ( B )= 1 6 Let P(A)=x, P(B)=y Since P(A B)^ = 1 3 aligned & 1-P(A B)= 1 3 & P(A B)= 2 3 & P(A)+P(B)-P(A B)= 2 3 & x+y- 1 6 = 2 3 x+y= 5 6 aligned Now, x ( 5 6 -x )= 1 6 5 x-6 x^2=1 aligned & 6 x^2-5 x+1=0 & (2 x-1)(3 x-1)=0 & x= 1 2 or 1 3 P(A)= 1 2 or 1 3 aligned