A and B are two independent events such that P(A) = frac{1}{2} and P(B) = frac{1}{3} . Then P (neith

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14.Probability

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$A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{3}$. Then $P$ (neither $A$ nor $B$) is equal to

A

$2/3$

B

$1/6$

C

$5/6$

D

$1/3$

Solution

(d) $P ($ neither $A$ nor $B ) = P(\bar A \cap \bar B) = P(\bar A)\,.\,P(\bar B)$

$P(\bar A) = 1 – P(A) = 1 – \frac{1}{2} = \frac{1}{2}$

$P(\bar B) = 1 – P(B) = 1 – \frac{1}{3} = \frac{2}{3}$

$\therefore $ $P(\bar A).P(\bar B) = \frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$.

Standard 11

Mathematics

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