Question

Let $X$ denote the number of time tail appear in $n$ tosses of a fair coin. If $P(X=1),P(X=2)$ and $P(X=3)$ are in A.P., then value of $n$ is

• A. $9$
• B. $2$
• C. $7$
• D. None of these

Answer 1

Answer: (C)

$7$

$P\left(T\right)=P\left(\overline{T}\right)=\frac{1}{2}$
$\therefore$ Using $P(X=r){=}^n{C}_r{\left(\frac{1}{2}\right)}^2$
Given, $2P(x=2)=P(X=1)+P(X=3)$
${2.}^n{C}_2{=}^0{C}_1{+}^n{C}_3$
$\Rightarrow n^2-9n+14=0$ $\Rightarrow n=7,2$
$\therefore n=7$ if $n=2$ there exist only three terms $\therefore n\ne 2.$