Q268 / 269 · NDA 2025 (Phase 1) · Mathematics
Let $X$ be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials $(n)$?
- A$500$
- Correct answerB$1000$
- C$1500$
- D$2000$
Solution
Let $n$ be the number of trials, $p$ be the probability of success, and $q$ be the probability of failure.
Given mean $= np = 200$
Given variance $= npq = 160$
Dividing variance by mean:
$\dfrac{npq}{np} = \dfrac{160}{200}$
$q = \dfrac{4}{5}$
Since $p + q = 1$, we have $p = 1 - \dfrac{4}{5} = \dfrac{1}{5}$
Substituting the value of $p$ in the mean equation:
$n \times \dfrac{1}{5} = 200$
$n = 1000$
Given mean $= np = 200$
Given variance $= npq = 160$
Dividing variance by mean:
$\dfrac{npq}{np} = \dfrac{160}{200}$
$q = \dfrac{4}{5}$
Since $p + q = 1$, we have $p = 1 - \dfrac{4}{5} = \dfrac{1}{5}$
Substituting the value of $p$ in the mean equation:
$n \times \dfrac{1}{5} = 200$
$n = 1000$
Hence, the correct answer is option: 'B'.