Question

A coin is tossed a times, what is the chance that the head will present itself an odd number of times?

Answer 1

As we know, $n\left(S\right)=2^{100}$

$n\left(E\right)=$ No. of favorable ways $={}^{100}{C}_1+{}^{100}{C}_3+...{}^{100}{C}_{99}=2^{100-1}=2^{99}$

$[\because {}^n{C}_1+{}^n{C}_3+{}^n{C}_5+...........................=2^{n-1}]$

$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{2^{99}}{2^{100}}=\frac{1}{2}$