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14.Probability
medium
જો $P(B) = \frac{3}{4}$, $P(A \cap B \cap \bar C) = \frac{1}{3}{\rm{ }}$ અને $P(\bar A \cap B \cap \bar C) = \frac{1}{3},$ તો $P(B \cap C)$ = . . .
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
