A random variable (X ) has the probability distribution ( array lllllll X=x_i & 1 & 2 & 3 & 4 & 5 & 6 P (X=x_i ) & 0.2 & 0.3 & 0.12 & 0.1 & 0.2 & 0.08 array ) If (A= x_i / x_i . ) is a prime number , (B= x_i / x_i < 4 ) are two events, then (P(A B)= )

Step-by-step solution

The given probability distribution for random variable (x ) ( array lllllll x=x_i & 1 & 2 & 3 & 4 & 5 & 6 P (X=x_i ) & 0.2 & 0.3 & 0.12 & 0.1 & 0.2 & 0.08 array ) and two events (A= x_i x_i . ) is a prime number ( ) (= 2,3,5 ) and (B= x_i x_i < 4 = 1,2,3 ) So, ( aligned & P(A B)=P(X=1)+P(X=2)+P(X=3)+P(X=5) & =0.2+0.3+0.12+0.2=0.82 aligned ) Hence, option (3) is correct.