A fair coin is tossed 100 times. The chance of getting a head even number of times is

Step-by-step solution

Given n=100 tosses of a fair coin with p=q= 1 2 , the number of heads X follows a binomial distribution. The probability of an even number of heads is given by the sum of even binomial coefficients: P( even heads ) = ( 1 2 )¹⁰⁰ [ 100 0 + 100 2 + + 100 100 ] Using the identity that the sum of even-indexed binomial coefficients equals 2^ n-1 , we substitute n=100 to obtain 2⁹⁹ . P( even heads ) = 1 2¹⁰⁰ 2⁹⁹ = 1 2 The probability of obtaining an even number of heads is exactly 1 2 . Answer: C