One hundred identical coins, each with probability p of showing up heads a

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 50 coins is equal to that head showing 51 coins, then the value of p is

Options:

A . 12

B . 49101

C . 50101

D . 51101

Answer: Option D
:
D
Let P1 and P2 be the respectively be the probability of heads showing 50 coins and head showing 51 coins

P_{1} = 100 C_{50} p^{50} (1 - p)^{50} a n d P_{2} = 100 C_{51} p^{51} (1 - p)^{49}

G i v e n P_{1} = P_{2}

\Rightarrow 100 C_{50} p^{50} (1 - p)^{50} = 100 C_{51} p^{51} (1 - p)^{49}

\Rightarrow \frac{1 - p}{p} = \frac{50}{51} \Rightarrow p = \frac{51}{101} .

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