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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 101 P is

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answer is 51.

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Detailed Solution

$W e h a v e 100 C_{50} P^{50} {(1 - P)}^{50} = 100 C_{51} P^{51} {(1 - P)}^{49}$
$\begin{array}{l} \Rightarrow \frac{1 - P}{P} = \frac{100!}{51! 49!} \times \frac{50! .50!}{100!} \\ \Rightarrow \frac{1 - P}{P} = \frac{50}{51} \\ \Rightarrow P = \frac{51}{101} \end{array}$

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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 101 P is