Q86 / 150 · MHT CET 2021 (22 Sep Shift 1) · Mathematics

A random variable $X \sim B(n, p)$, if values of mean and variance of $\mathrm{X}$ are 18,12 respectively, then $\mathrm{n}=$

  • Correct answer
    A
    54
  • B
    18
  • C
    12
  • D
    55

Solution

We have $n p=18$ and $n p q=12$ $$ \begin{aligned} & \therefore \mathrm{q}=\frac{12}{18}=\frac{2}{3} \quad \Rightarrow \mathrm{p}=1-\frac{2}{3}=\frac{1}{3} \\ & \therefore \mathrm{n}\left(\frac{1}{3}\right)=18 \quad \Rightarrow \mathrm{n}=54 \end{aligned} $$

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

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