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Question

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 find the value of p.

Solution
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We have 100C50p50(1p)50=100C51p51(1p)49
or 1pp=100!51!49!×50!50!100!=5051
5151p=50p
51=50p+51p
101p=51
p=51101

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