Q79 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

A discrete random variable $X$ has the distribution $B(15, p)$. Given that $\operatorname{Var}(X)=3.15$. Then, the two possible values of $p$ are

  • A
    0,1
  • B
    $0.1,0.9$
  • C
    $0.4,0.6$
  • Correct answer
    D
    $0.3,0.7$

Solution

$\begin{aligned} & \text { Here, } n=15, q=1-p \\ & \operatorname{Var}(X)=315 ; n p q=315 \\ & \quad 15 \times p(1-p)=315 \\ & \Rightarrow \quad p-p^2=0.21 \Rightarrow p^2-p+0.21=0 \\ & \Rightarrow \quad p^2-0.7 p-0.3 p+0.21=0 \\ & \Rightarrow \quad p(p-0.7)-0.3(p-0.7)=0 \\ & \quad p=0.7,0.3\end{aligned}$

Hence, the correct answer is option: 'D'.

Relevant Questions