#### Question

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

#### Solution

In the given binomial distribution, *n *= 4 and

\[P(X = 0) = \frac{16}{81} \]

\[\text{ Binomial distribution is given by} \]

\[P(X = 0) = ^ {4}{}{C}_0\ p^0 q^{4 - 0} = q^4 \]

\[\text{ We know that } P(X = 0) = \frac{16}{81} \]

\[ \therefore q^4 = \frac{16}{81}\]

\[ \Rightarrow q^4 = \left( \frac{2}{3} \right)^4 \]

\[ \Rightarrow q = \frac{2}{3}\]

\[\text{ Binomial distribution is given by} \]

\[P(X = 0) = ^ {4}{}{C}_0\ p^0 q^{4 - 0} = q^4 \]

\[\text{ We know that } P(X = 0) = \frac{16}{81} \]

\[ \therefore q^4 = \frac{16}{81}\]

\[ \Rightarrow q^4 = \left( \frac{2}{3} \right)^4 \]

\[ \Rightarrow q = \frac{2}{3}\]

Is there an error in this question or solution?

Solution If in a Binomial Distribution N = 4 and P (X = 0) = 16 81 , Find Q. Concept: Bernoulli Trials and Binomial Distribution.