Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# If in a Binomial Distribution N = 4, P (X = 0) = 16 81 , Then P (X = 4) Equals (A) 1 16 P (B) 1 81(C) 1 27 (D) 1 8 - Mathematics

MCQ

If in a binomial distribution n = 4, P (X = 0) = $\frac{16}{81}$, then P (X = 4) equals

#### Options

• $\frac{1}{16}$

• $\frac{1}{81}$

•  $\frac{1}{27}$

•  $\frac{1}{8}$

#### Solution

$\frac{1}{81}$ In the given binomial distribution, = 4 and

$P(X = 0) = \frac{16}{81}$
$\text{ Binomial distribution is given by }$
$P(X = 0) =^ {4}{}{C}_0 \ p^0 q^{4 - 0} = q^4$
$\text{ We know that P } (X = 0) = \frac{16}{81}$
$\therefore q^4 = \frac{16}{81}$
$\Rightarrow q^4 = \left( \frac{2}{3} \right)^4$
$\Rightarrow q = \frac{2}{3}$
$\therefore p = 1 - \frac{2}{3} = \frac{1}{3}$
$\text{ Then } , P(X = 4) = ^{4}{}{C}_4 \ p^4 q^{4 - 4}$
$= \left( \frac{1}{3} \right)^4$
$= \frac{1}{81}$

Concept: Bernoulli Trials and Binomial Distribution
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 2 | Page 28