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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-II

  • question_answer
    The probability of India winning a test match against Westinies 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.

    A) 2/3

    B) 1/2

    C) 1/4

    D) 1/8

    Correct Answer: C

    Solution :

    [c] Since, India?s second win occurs at the third test. Therefore, the sample space is \[=[LWW,WLW]\] Where, L = losing the test W = winning the test. \[\therefore \]P (India?s win occur at the 3rd test) \[=P(LWW)+P(WLW)\] \[=P(L)P(W)P(W)+P(W)P(L)P(W)\] (\[\therefore \] Prob. From match to match is independent). \[=\left( \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} \right)+\left( \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2} \right)\] (Given) \[=\frac{1}{8}+\frac{1}{8}=\frac{2}{8}=\frac{1}{4}\]


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