If A and B an two events such that P,(A cup B) = frac{5}{6} , P,(A cap B) = frac{1}{3} and P,(bar B)

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14.Probability

easy

If $A$ and $B$ an two events such that $P\,(A \cup B) = \frac{5}{6}$,$P\,(A \cap B) = \frac{1}{3}$ and $P\,(\bar B) = \frac{1}{3},$ then $P\,(A) = $

A

$\frac{1}{4}$

B

$\frac{1}{3}$

C

$\frac{1}{2}$

D

$\frac{2}{3}$

Solution

(c) $P(A) = P(A \cap B) + P(A \cup B) – P(B)$

$ = \frac{1}{3} + \frac{5}{6} – \frac{2}{3} = \frac{3}{6} = \frac{1}{2}.$

Standard 11

Mathematics

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