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If $A$ and $B$ are two events such that $P(A \cup B)=\frac{3}{4}$,
$P(A \cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{2}{3}$, then what is $P(B)$ equal to?
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$P(A \cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{2}{3}$, then what is $P(B)$ equal to?
Solution:
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Verified Answer
The correct answer is:
$\frac{2}{3}$
$\begin{array}{ll} & \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{3}{4} \\ & \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{4} \\ & \mathrm{P}(\overline{\mathrm{A}})=\frac{2}{3}, \mathrm{P}(\mathrm{A})=\frac{1}{3} \\ \therefore \quad & \mathrm{P}(\mathrm{B})=\frac{3}{4}-\frac{1}{3}+\frac{1}{4}=\frac{9-4+3}{12}=\frac{\not 8}{12}=\frac{2}{3} \\ \therefore & \text { Option (b) is correct. }\end{array}$
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