Question

A fair coin is tossed 100 times. What is the probability of getting tail on tossing odd number of times

Answer 1

Let X denote the number of tails. Then X is a

binomial variate with parameters

n 100 P 1/2

P(x=r) = 100Cr(1/2)^

100r 0,1, 2, . .100

Required probability

P(x 1)P(x = 3)+... .P(x 99)

= (1/2)^100[ 100C1+100C3+100C5+...+100C99]

(1/2) 100x (2^99)

=1/2