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 heads on 51 coins; then the value of \(P\) is
According to the given condition, \[\] \({ }^{100} C_{50}(p)^{50}(1-p)^{50}={ }^{100} C_{51}(p){ }^{51}(1-p)^{49}\) \[\] \(\frac{100!}{50!50!}(1-p)=\frac{100!}{51!49!} \cdot p\) \[\] \(\frac{1-p}{50}=\frac{p}{51} \Rightarrow 51-51 p=50 p\) \[\] or \(p=\frac{51}{101}\) \[\] Choice (d)\[\]
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