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Question: Answered & Verified by Expert
The mean and variance of a random variable $\mathrm{X}$ having binomial distribution are 4 and 2 respectively, then $\mathrm{P}$ $(\mathrm{X}=1)$ is
MathematicsProbabilityJEE MainJEE Main 2003
Options:
  • A
    $\frac{1}{4}$
  • B
    $\frac{1}{32}$
  • C
    $\frac{1}{16}$
  • D
    $\frac{1}{8}$
Solution:
2529 Upvotes Verified Answer
The correct answer is:
$\frac{1}{32}$
$\left.\begin{array}{c}\mathrm{np}=4 \\ \mathrm{npq}=2\end{array}\right\} \Rightarrow \mathrm{q}=\frac{1}{2} \cdot \mathrm{p}=\frac{1}{2}, \mathrm{n}=8$
$\mathrm{p}(\mathrm{X}=1)={ }^8 \mathrm{C}_1\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)^7=8 \cdot \frac{1}{2^8}=\frac{1}{2^5}=\frac{1}{32}$

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