Q79 / 160 · AP EAMCET 2022 (08 Jul Shift 2) · Mathematics

In a Binomial distribution, if $p=q$ and $n \geq 4$, then $2^n P(X=5)=$

  • A
    $5$
  • B
    ${ }^n \mathrm{C}_2$
  • C
    $10$
  • Correct answer
    D
    ${ }^n C_5$

Solution

Given, $p=q$ $\begin{aligned} & \because \quad p+q=1 \\ & \Rightarrow \quad p=q=\frac{1}{2}\end{aligned}$ Now, $2^n P(X=5)$ $\begin{aligned} & =2^n \cdot{ }^n C_5(P)^{n-5}(q)^5=2^n \cdot{ }^n C_5\left(\frac{1}{2}\right)^{n-5} \cdot\left(\frac{1}{2}\right)^5 \\ & =2^n \cdot{ }^n C_5\left(\frac{1}{2}\right)^n={ }^n C_5\end{aligned}$

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

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