An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is

Step-by-step solution

P(A)= 2 5 For independent events, aligned & P(A B)=P(A) P(B) P(A B) 2 5 & P(A B)= 1 10 , 2 10 , 3 10 , 4 10 & (i) P(A B)= 1 10 & P(A) P(B)= 1 10 & P(B)= 1 10 5 2 = 1 4 , not possible. & (ii) P(A B)= 2 10 2 5 P(B)= 2 10 & P(B)= 5 10 , outcomes of B=5 aligned (iii) aligned & P(A B)= 3 10 P(A) P(B)= 3 10 & 2 5 P(B)= 3 10 & P(B)= 3 4 , not possible aligned (iv) aligned & P(A B)= 4 10 & P(A) P(B)= 4 10 & P(B)=1, outcomes of B=10 . aligned