One hundred identical coins each with probability p of

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One hundred identical coins each with probability p of showing up head are tossed. If 0 < p < 1 and the probability of heads showing on 50 coins is equals to that of heads on 51 coins. Then the value of p, is ?

1. 1/2
2. 49/101
3. 50/101
4. 51/101

Correct Option: D

Let N be the number of coins showing heads.
∴ Probability when N equal to 50 = Probability when N equal to 51
⇒ ¹⁰⁰C₅₀ x P ⁵⁰ x (1 - p)⁵⁰ = ¹⁰⁰C₅₁ x (1 - p)⁴⁹
⇒ p = 51/101