# Suppose that A & b are mutually exclusive events. Then P(A)=.3 and P(B)=.5. What is the probability that either A or B occurs? A occurs but b doesn't. Both A and B occur. 1) Since the are mutually exclusive: P(A∪B)=P(A)+P(B)=.3+.5=.8 2) A occurs but B does not: .3 3) Both A and B occur: Since they are mutually exclusive: P(A∩B)=0 or the empty set. Are these correct

Suppose that $A$ & $B$ are mutually exclusive events. Then $P\left(A\right)=.3$ and $P\left(B\right)=.5$. What is the probability that either $A$ or $B$ occurs? $A$ occurs but b doesn't. Both $A$ and $B$ occur.
1) Since the are mutually exclusive:
$P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)=.3+.5=.8$
2) $A$ occurs but $B$ does not: $.3$
3) Both $A$ and $B$ occur:
Since they are mutually exclusive:
$P\left(A\cap B\right)=0$ or the empty set
Are these correct?
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Zara Pratt
We always have:
$P\left(A\right)=P\left(A\cap B\right)+P\left(A\cap {B}^{C}\right)$
but now that $A$ and $B$ are mutually exclusive, we have $P\left(A\cap B\right)=0$
thus: $P\left(A\cap {B}^{C}\right)=P\left(A\right)$