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JEE Main & Advanced JEE Main Paper Phase-I Held on 07-1-2020 Morning

  • question_answer
    An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected value of X, is [JEE MAIN Held on 07-01-2020 Morning]

    A) \[\frac{3}{16}\]             

    B) \[-\frac{1}{8}\]

    C) \[-\frac{3}{16}\]

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

    Correct Answer: D

    Solution :

    [d]            
    k 3 4 5
    P(k) \[\frac{5}{32}\] \[\frac{2}{32}\] \[\frac{1}{32}\]
                \[\therefore \] For \[k=1\] or 2, \[\therefore \,P(k)=1-\frac{5}{32}-\frac{2}{32}-\frac{1}{32}=\frac{24}{32}\] Now expectation \[=\left( 3\times \frac{5}{32} \right)+\left( 4\times \frac{2}{32} \right)+\left( 5\times \frac{1}{32} \right)+(-1)\left( \frac{24}{32} \right)\] \[=\frac{4}{32}=\frac{1}{8}\]


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