JEE Main 2015 (Online) 11th AprilQuestion 1
If the mean and the variance of a binomial variate $X$ are $2$ and $1$ respectively, then the probability that $X$ takes a value greater than or equal to one is :
Probability
Solution
$np=2$, $npq=1\Rightarrow q=\frac12,\ p=\frac12,\ n=4$. $P(X\ge1)=1-\left(\frac12\right)^4=\frac{15}{16}$.