Question

The mean and variance of a binomial distribution are $4$ and $3$ respectively. Fix the distribution and find $P(X\ge 1)$.

Answer 1

Fact: In binomial distribution , mean $=np$ and variance $=npq$

Here given $np=4$ and $npq=3$

So $q=\frac{3}{4}\Rightarrow p=1-p=\frac{1}{4}$

Thus $n=16$

Hence $P(X\ge 1)=1-P(X=0)=1{-}^{16}{C}_0{p}^0{q}^{16}=1-{\left(\frac{3}{4}\right)}^{16}$