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

Step-by-step solution

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