If and , then find the value of .

Engineering

Mathematics

Conditional Probability

Question

If $P (A \cup B) = \frac{3}{4}$ and $P (\bar{A}) = \frac{2}{3}$ , then find the value of $P (\bar{A} \cap B)$ .

$\frac{3}{2}$

$\frac{1}{2}$

$\frac{5}{12}$

None of these

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Since A⋂B and A are mutually exclusive events such that
$A \cup B = (\bar{A} \cap B) \cup A$

or $P (A \cup B) = P (\bar{A} \cap B) + P (A)$

or $\frac{3}{4} = P (\bar{A} \cap B) + 1 - \frac{2}{3}$
or $P (\bar{A} \cap B) = \frac{5}{12}$

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