a fair coin tossed untill a head appear for the first time

a fair coin tossed untill a head appear for the first time . what are the chances of that happening on an odd numbered toss.

Solution

let head appeared first time at 2m+1 toss. This means, we get Tails up to 2m toss. The chances of that happening on an odd numbered toss is (0.5^2m)(0.5) or (0.5)^(2m+1)