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If $A$ and $B$ are mutually exclusive events with $P(A)=0.6$ and $P(B)=0.3$, find the following:

(a) $P(A \cup B)$
(b) $P\left(A^{\prime} \cap B\right)$
(c) $P\left(A^{\prime} \cup B^{\prime}\right)$
(d) $P(A \mid B)$
(e) $P\left(B^{\prime} \mid A^{\prime}\right)$
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(a) $P(A \cup B)=P(A)+P(B)-P(A \cap B)=.6+.3-0=.9$
(b) $P\left(A^{\prime} \cap B\right)=P(B)=.3$
(c) $P\left(A^{\prime} \cup B^{\prime}\right)=P\left(A^{\prime}\right)+P\left(B^{\prime}\right)-P\left(A^{\prime} \cap B^{\prime}\right)=.4+.7-.1=1.0$
(d) $P(A \mid B)=P(A \cap B) / P(B)=0$
(e) $P\left(B^{\prime} \mid A^{\prime}\right)=P\left(B^{\prime} \cap A^{\prime}\right) / P\left(A^{\prime}\right)=.1 / .4=.25$
by Diamond (40,719 points)

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