# Given P(A) =0.5 and P(B) =0.4 do the following. (a) If A and B are mutually exclusive, compute...

## Question:

Given P(A) =0.5 and P(B) =0.4 do the following.

(a) If A and B are mutually exclusive, compute P(A or B)

(b) If P(A and B) =0.3, compute P(A or B)

## Mutually Exclusive and Nonexclusive Events:

If {eq}A {/eq} and {eq}B {/eq} are two mutually exclusive events, then the probability of {eq}A {/eq} or {eq}B {/eq} is the addition of the probability of {eq}A {/eq} and the probability of {eq}B {/eq} i.e., {eq}P(A \bigcup B) = P(A) + P(B) {/eq}. If {eq}A {/eq} and {eq}B {/eq} are two mutually nonexclusive events, then the probability of {eq}A {/eq} or {eq}B {/eq} is the addition of the probability of {eq}A {/eq} and the probability of {eq}B {/eq} minus the probability of both{eq}A {/eq} and{eq}B {/eq} i.e., {eq}P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B) {/eq}.

(a) If A and B are mutually exclusive, compute P(A or B)

• {eq}P(A \bigcup B) = P(A) + P(B) = 0.5 + 0.4 = 0.9 {/eq}

(b) If P(A and B) =0.3, compute P(A or B)

• {eq}P(A \bigcup B) = P(A) + P(B) - P(A \bigcap B) = 0.5 + 0.4 - 0.3 = 0.6 {/eq} 