If n coins are tossed simultaneously, the probability of getting head an odd number of times is

Getting on odd number of heads

$n\left(S\right)=2^n$

$n\left(A\right){=}^n{C}_1{+}^n{C}_3{+}^n{C}_5+\cdots +$

$\left\{{\because }^n{C}_0{+}^n{C}_1{+}^n{C}_2{+}^n{C}_3+\cdots {+}^n{C}_n=2^n\right\}$

${}^{2n}{C}_1{+}^{2n}{C}_3{+}^{2n}{C}_5+\cdots =2^n$

${}^n{C}_0{=}^n{C}_1{.}^n{C}_1{=}^n{C}_{n-1}\cdots$

${\therefore }^n{C}_1{+}^n{C}_3{+}^n{C}_5+\cdots =\frac{2^n}{2}=2^{n-1}$

$P\left(A\right)=\frac{2^{n-1}}{2^n}=\frac{1}{2}$