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

\[P(X = 0) = \frac{16}{81} \]
\[\text{ Binomial distribution is given by} \]
\[P(X = 0) = ^ {4}{}{C}_0\ p^0 q^{4 - 0} = q^4 \]
\[\text{ We know that } P(X = 0) = \frac{16}{81} \]
\[ \therefore q^4 = \frac{16}{81}\]
\[ \Rightarrow q^4 = \left( \frac{2}{3} \right)^4 \]
\[ \Rightarrow q = \frac{2}{3}\]