Question

If event A and B are mutually exclusive. P (A)> 0, P (B )> 0
Are A and B independent? Show/explain then crazy proof!

Answer 1

If A and B are mutually exclusive, it means that they cannot both happen. Therefore
\[\large P(A\ and\ B)=0\]
If A and B are independent events, then
\[\large P(A\ and\ B\ occur)=P(A) \times P(B)\]
But P(A) and P(B) are both greater than one, therefore P(A) * P(B) cannot equal zero.
Thus A and B do not meet the test for independence.