JEE Main & Advanced Sample Paper JEE Main Sample Paper-4

  • question_answer
    One hundred identical coins, each with probability p, of showing up heads are tossed. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of the heads showing on 51 coins, then p =

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

    B) \[\frac{49}{101}\]

    C) \[\frac{50}{101}\]                                            

    D) \[\frac{51}{101}\]

    Correct Answer: D

    Solution :

    Here \[n=100,p=p,q=1-p\] Given, P(50) = P(5 \[\Rightarrow \]\[^{100}{{C}_{50}}{{p}^{50}}{{(1-p)}^{50}}{{=}^{10}}{{C}_{51}}{{p}^{51}}{{(1-p)}^{49}}\] \[\Rightarrow \]\[\frac{100!}{50!50!}(1-p)=\frac{100!}{51!49!}p\]\[\Rightarrow \]\[51(1-p)=50p\] \[\Rightarrow \]\[p=\frac{51}{101}\]

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