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Q.

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

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a

12

b

49101

c

50101

d

51101

answer is D.

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Detailed Solution

P(x=50)=P(x=51)⇒100C50(p)50(1−p)50=100C51(p)51(1−p)49       [ formula P( x=r ) =c(n,r)  qn-r·pr   ]                           ⇒1−pp=5051                                       (  since  C(n,r )C(n,r-1)=n-r+1r )⇒p=51101
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