A coin is tossed $n$ times. What is the probability of getting odd number of heads? 
A coin is tossed $n$ times. What is the probability of getting odd number of heads?

I started this chapter sometimes ago and faced in front of a tough problem. At first I started considering cases. Case-I : The probability of getting 1 head.Case-II : The probability of getting 3 head and so on. But there are many cases. So how can I solved this . Please help me. Thank you!

The probability of getting $k$ heads is $\binom{n}{k}2^{-n}$. So the required probability is $$\sum_{k=0}^{\lfloor\frac{n-1}{2}\rfloor}\binom{n}{2k+1}2^{-n}=2^{-n}\times2^{n-1}=\frac{1}{2}$$
