14.Probability
medium

If $P(B) = \frac{3}{4}$, $P(A \cap B \cap \bar C) = \frac{1}{3}{\rm{ }}$ and $P(\bar A \cap B \cap \bar C) = \frac{1}{3},$ then $P(B \cap C)$ is

A

$\frac{1}{{12}}$

B

$\frac{1}{6}$

C

$\frac{1}{{15}}$

D

$\frac{1}{9}$

(IIT-2003)

Solution

(a) From Venn diagram, we can see that
$P(B \cap C)\, = P(B) – P(A \cap B \cap \bar C) – P(\bar A \cap B \cap \bar C)$
$ = \frac{3}{4} – \frac{1}{3} – \frac{1}{3} = \frac{1}{{12}}.$

Standard 11
Mathematics

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