Question

If in a binomial distribution n = 4 and P (X = 0) = $\frac{16}{81}$, find q.

Answer 1

In the given binomial distribution, n = 4 and
$$\begin{gathered} P(X=0)=\frac{16}{81} \\ \mathrm{Binomial}\mathrm{distribution}\mathrm{is}\mathrm{given}\mathrm{by} \\ P(X=0)={}^{4}C_0{p}^0{q}^{4-0}=q^4 \\ \text{We}\mathrm{know}\mathrm{that}P(X=0)=\frac{16}{81} \\ \therefore q^4=\frac{16}{81} \\ \Rightarrow q^4={\left(\frac{2}{3}\right)}^4 \\ \Rightarrow q=\frac{2}{3} \end{gathered}$$