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JEE Main & Advanced Mathematics Probability Question Bank Definition of probability

  • question_answer
    The probability of India winning a test match against West Indies is \[\frac{1}{2}\]. Assuming independence from match to match, the probability that in a 5 match series India's second win occurs at the third test, is          [IIT 1995; Pb. CET 2003]

    A)                 \[\frac{2}{3}\]       

    B)                 \[\frac{1}{2}\]

    C)                 \[\frac{1}{4}\]       

    D)                 \[\frac{1}{8}\]

    Correct Answer: C

    Solution :

               The sample space is \[[LWW,\,\,WLW]\]            \[\therefore \,\,\,P(LWW)+P(WLW)\]            = Probability that in 5 match series, it is India?s second win                 \[=P(L)P(W)P(W)+P(W)P(L)P(W)\]\[=\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4}.\]


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