proof question with probability show that events are not ind

proof question with probability, show that events are not independet

Let A_1 and A_2 be mutually exclusive events such that P[A_1]P[A_2]greaterthan0. Show that these events are not independent.

Solution

Given A1 and A2 mutually exclusive events.

since the events mutully exclusive A1 and A2 = null

P(A1 and A2 ) =0;

If A and B are independent then P(A1 and A2) = P(A1) P(A2)

Therefore P(A1 and A2) =P(A1) P(A2) = 0

But given P(A1) P(A2) >0

Therefore the events are not independent