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Probability of solving specific problem independently by A and B are 1 by 2 and 1 by 3 respectively, (ii) exactly one of them solves the problem

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

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  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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