A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is

Question

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is, 15 2 13, 15 2 14, 15 2 12, 15 2 8

MARKS App · Accepted Answer

Let the coin be tossed n -times P H = P T = 1 2 P ( 7 heads) = C 7 n 1 2 n - 7 1 2 7 = C 7 n 2 n P ( 9 heads) = C 9 n 1 2 n - 9 1 2 9 = C 9 n 2 n P ( 7 heads) = P ( 7 heads) C 7 n = C 9 n ⇒ n = 16 P ( 2 heads) = C 2 16 1 2 14 1 2 2 = 15 × 8 2 16 P ( 2 heads) = 15 2 13

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