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JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    A biased coin with probability \[-p(0<p<1)\]of falling tails is tossed until a tail appears for the first time. If the probability that tail comes in odd number of trials is 2/3, then p equals

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

    B)  \[\frac{1}{3}\]

    C)  \[\frac{3}{4}\]                                  

    D)  \[\frac{1}{2}\]

    Correct Answer: D

    Solution :

     \[P(T)=p;P(H)=1-p\] \[\therefore \]Required probability \[=p(Tor\,HHTor\,HHHHT\,or...)\] \[=p+{{(l-p)}^{2}}p+{{(1-p)}^{4}}p+...\] \[=\frac{p}{1-{{(1-p)}^{2}}}\] \[=\frac{p}{2p-{{p}^{2}}}=\frac{2}{3}\] \[\Rightarrow \]               \[p=\frac{1}{2}\]


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