A biased coin with probability $ p, 0 \( \frac{2}{5} $, then $ p $ equal to

Question

A biased coin with probability $ p, 0 \( \frac{2}{5} $, then $ p $ equal to, $ \frac{1}{3} $, $ \frac{2}{3} $, $ \frac{2}{5} $, $ \frac{3}{5} $

MARKS App · Accepted Answer

Let q = 1 - p . Since, head appears first time in an even throw 2 or 4 or 6 ∴ 2 5 = q p + q 3 p + q 5 p + . . . ∴ 2 5 = q p 1 - q 2 ⇒ 2 5 = 1 - p p 1 - 1 - p 2 ⇒ 2 5 = 1 - p 2 - p ⇒ 4 - 2 P = 5 - 5 P ⇒ p = 1 3

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