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10th Class Mathematics Probability Question Bank Probability

  • question_answer
    The probability that A can win a race is\[\frac{3}{8}\] and the probability that B can win it is\[\frac{1}{6}\]. If both run in a race, what is the probability that one of them will win the race, assuming that both cannot win together?

    A)  \[\frac{17}{24}\]                                             

    B)  \[\frac{15}{24}\]

    C)  \[\frac{13}{24}\]                             

    D)         \[\frac{11}{24}\]

    Correct Answer: C

    Solution :

     Let A be the event that A wins and B be the event that B wins. \[\therefore \]P (one of them will win) \[=P(A\cup B)\] \[=\text{P(A)}+\text{P(B)}\] (Since, A and B are mutually exclusive.) \[=\frac{3}{8}+\frac{1}{6}=\frac{13}{24}\]


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