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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • 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 match series Indias second win occurs at the third test is:

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

    B)  \[\frac{1}{4}\]

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

    D)  \[\frac{2}{3}\]

    Correct Answer: B

    Solution :

                    Required probability \[P(A{{ & }_{1}}A_{2}^{}{{A}_{3}})+P(A_{1}^{},{{A}_{2}},{{A}_{3}})\] \[=P({{A}_{1}})P(A_{2}^{})P({{A}_{3}})+P(A_{1}^{})P({{A}_{2}})P({{A}_{3}})\] \[={{\left( \frac{1}{2} \right)}^{3}}+{{\left( \frac{1}{2} \right)}^{3}}\] \[=\frac{1}{8}+\frac{1}{8}\] \[=\frac{2}{8}\] \[=\frac{1}{4}\]


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