Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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# If in a Binomial Distribution N = 4 and P (X = 0) = 16 81 , Find Q. - Mathematics

#### Question

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

#### Solution

In the given binomial distribution, = 4 and

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