Answer to Question #208964 in Statistics and Probability for mimi

Question

If events A and B are mutually exclusive, then P.A and B/ D 0.

Answer 1

Two events A and B are mutually exclusive, or disjoint, if $A\cap B=\empty,$ that is, if A and B have no elements in common.

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

$$P(B|A)=\dfrac{P(A\cap B)}{P(A)}$$

$$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$$

Since $P(A)\not=0, P(B)\not=0,$ then for two mutually exclusive events $A$ and $B$

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

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