Question

20. Suppose that two events, A and B, are mutually exclusive and PrB>. Under what conditions will A and B be independent?

Answer 1

Two events A and B are said to be Mutually exclusive if,

$P(A\cup B) = P(A) + P(B)$

or,

$P(A\cap B) = 0$

Two events are said to be independent if ,

$P(A\cap B) = P(A)P(B)$

Since they are also mutually independent so,

$P(A)P(B)= 0$

$\Rightarrow P(A)= 0$            since it is given that P(B)>0

So, P(A) = 0 is the required condition