Question

The probability of selecting a male or a female is same. If the probability that in an office of n persons (n − 1) males being selected is $\frac{3}{2^{10}}$, the value of n is
(a) 5
(b) 3
(c) 10
(d) 12

Answer 1

(d) 12

Let X be the number of males.
$$\begin{gathered} p\mathit{}=q=\frac{1}{2}\left(\mathrm{given}\right) \\ P(X=n-1)={}^{n}C_{n-1}{\left(p\right)}^{\mathrm{n}-1}{q}^1=\frac{3}{2^{10}} \\ \Rightarrow n{\left(\frac{1}{2}\right)}^n=\frac{3}{2^{10}} \\ \Rightarrow n{\left(\frac{1}{2}\right)}^n=3\left(\frac{2^2}{2^{12}}\right) \\ \Rightarrow n{\left(\frac{1}{2}\right)}^n=12{\left(\frac{1}{2}\right)}^{12} \\ \mathrm{By}\mathrm{comparing}\mathrm{the}\mathrm{two}\mathrm{sides},\mathrm{we}\mathrm{get}n=12 \end{gathered}$$