# Given P(A) = 0.25, P(B) = 0.38, and P(A or B) = 0.63, are events A and B mutually exclusive?

## Question:

Given {eq}P(A) = 0.25,\ P(B) = 0.38 {/eq}, and {eq}P(A \cup B) = 0.63 {/eq}, are events {eq}A {/eq} and {eq}B {/eq} mutually exclusive?

## Mutually Exclusive Events:

Two events A and B are said to be mutually exclusive events if the occurrence of one event precludes the occurrence of other event.

{eq}P(A \cap B)=0 {/eq}

We have P(A)=0.25 P(B)=0.38 and {eq}P(A \cup B)=0.63=0.25+0.38 -P(A \cap B) \\ P(A \cap B)=0 {/eq}

So we can say that A and B are mutually exclusive events.