# Q.14     Probability of solving specific problem independently by A and B are $\frac{1}{2}$  and $\frac{1}{3}$ respectively. If both try to solve the problem independently, find the probability that                (ii) exactly one of them solves the problem

$P(A)=\frac{1}{2}$           and        $P(B)=\frac{1}{3}$

$P(A')=1-P(A)$,      $P(B')=1-P(B)$

$P(A')=1-\frac{1}{2}=\frac{1}{2}$  ,           $P(B')=1-\frac{1}{3}=\frac{2}{3}$

probability that exactly one of them solves the problem $=P(A\cap B') + P(A'\cap B)$

probability that exactly one of them solves the problem  $=P(A).P(B')+P(A')P(B)$

$=\frac{1}{2}\times \frac{2}{3}+\frac{1}{2}\times \frac{1}{3}$

$= \frac{2}{6}+\frac{1}{6}$

$= \frac{3}{6}=\frac{1}{2}$

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