100 identical coins, each with probability P of showing '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 50 coins, then find the value of P.
Pick one
A) 51/101.	B) 51/100	C) 32/81	D) None of these	E) Cannot be determined
Explanation :   Let X be the number of coins showing 'heads', then X follows a binomial distribution with parameters n = 100 and P.   As given, P(X=50) = P(X=51)   =&gt; 100C50P50(1-P)50 = 100C51P51(1-P)49 .   =&gt; 51/50 = P / (1-P)   =&gt; p = 51/101.   Hence, the value of p is 51/101.   51/101.nswer : 51/101.
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100 identical coins, each with probability P of showing '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 50 coins, then find the value of P.