A fair coin is tossed a fixed number of times. If the probability of getting 5 tails is same as the probability of getting 7 tails, then the probability of getting 3 tails is

Step-by-step solution

Given equal probabilities for exactly 5 and 7 tails in n coin tosses, we establish n 5 = n 7 after eliminating the common ( 1 2 )^n factor. Using the symmetry property n k = n n-k , the equality implies 5 + 7 = n , yielding n = 12 . The probability of exactly 3 tails is 12 3 ( 1 2 )¹² . Calculating 12 3 = 220 , we obtain P(X=3) = 220 2¹² = 55 2¹⁰ . This matches option B .