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

               (i) the problem is solved

Answers (1)

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

Since, problem is solved independently by A and B,

\therefore           P(A\cap B)=P(A).P(B)

               P(A\cap B)=\frac{1}{2}\times \frac{1}{3}

                 P(A\cap B)=\frac{1}{6}

  probability that the problem is solved = P(A\cup B)

         P(A\cup B)=P(A)+P(B)-P(A\cap B)

        P(A\cup B)=\frac{1}{2}+\frac{1}{3}-\frac{1}{6}

        P(A\cup B)=\frac{5}{6}-\frac{1}{6}

            P(A\cup B)=\frac{4}{6}=\frac{2}{3}