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10th Class Mathematics Probability Question Bank Probability

  • question_answer
    The probability that A can solve a problem is \[\frac{2}{3}\]and the probability that B can solve the same problem is \[\frac{3}{5}\]. Find the probability that at least one of A and B will be able to solve the problem.

    A)  \[\frac{12}{15}\]                                  

    B)  \[\frac{13}{15}\]

    C)  \[\frac{19}{45}\]                                  

    D)  None of these

    Correct Answer: B

    Solution :

    (b): \[P(A)=\frac{2}{3},P(B)=\frac{3}{5}\] Required probability \[=P(A\,\,or\,\,B)=P(A\cup B)\] be the events of solving the problem by A or B                                         \[=P(A)\,\,+P(\,B)-P(A)P(B)\]                         \[=\frac{2}{3}+\frac{3}{5}-\frac{2}{3}.\frac{3}{5}=\frac{13}{15}\]


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