One coin is thrown 100 times, then the probability of getting head in odd number is

Question

Aicharya · Accepted Answer

$n=100, p=\frac{1}{2}, q=\frac{1}{2}$ $p(x=r$ where $r$ is odd $)=\sum_{r=	ext { odd }}^n C_r p^r q^{n-r}$ $\begin{aligned} & =\sum_{r=	ext { odd }}^{100} C_r\left(\frac{1}{2}ight)^r\left(\frac{1}{2}ight)^{100-r} \ & =\left(\frac{1}{2}ight)^{100} \sum_{r=	ext { odd }}{ }^{100} C_r \ & =\left(\frac{1}{2}ight)^{100} 	imes 2^{99}=\frac{1}{2}\end{aligned}$

One coin is thrown 100 times, then the probability of getting head in odd number is

Solution