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JEE Main & Advanced AIEEE Solved Paper-2002

  • question_answer
    The probability of India winning a test match against West-Indies is \[1/2\] assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is

    A) \[1/8\]                    

    B) \[1/4\]

    C) \[1/2\]   

    D)           \[2/3\]

    Correct Answer: B

    Solution :

       Let \[{{A}_{1}},{{A}_{2}}\] and \[{{A}_{3}}\] be the events of match winning in first, second and third match respectively and whose probabilities are                    \[P({{A}_{1}})=P({{A}_{2}})=P({{A}_{3}})=\frac{1}{2}\] Required probability \[=P({{A}_{1}}\,A{{'}_{2}}{{A}_{3}})+P(A_{1}^{'}\,{{A}_{2}}\,{{A}_{3}})\] \[=P({{A}_{1}})P({{A}_{2}}')P({{A}_{3}})+P({{A}_{1}}')P({{A}_{2}})P({{A}_{3}})\] \[={{\left( \frac{1}{2} \right)}^{3}}+{{\left( \frac{1}{2} \right)}^{3}}=\frac{1}{8}+\frac{1}{8}=\frac{1}{4}\]


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