# If X Follows Binomial Distribution with Parameters N = 5, P and P(X = 2) = 9p(X = 3), Then Find the Value of P. - Mathematics

If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.

#### Solution

$\text{ We have } ,$
$\text{ X follows binomial distribution with parameters n = 5, p and } P\left( X = 2 \right) = 9P\left( X = 3 \right) .$
$\text{ So} , P\left( X = r \right) = ^{5}{}{C}_r p^r q^\left( 5 - r \right) , \text{ where } r = 0, 1, 2, 3, 4, 5 \text{ and } q = 1 - p$
$\text{ As,} P\left( X = 2 \right) = 9P\left( X = 3 \right)$
$\Rightarrow ^{5}{}{C}_2 p^2 q^3 = 9 ^{5}{}{C}_3 p^3 q^2$
$\Rightarrow 10 p^2 q^3 = 9 \times 10 p^3 q^2$
$\Rightarrow q = 9p$
$\Rightarrow 1 - p = 9p \left[ \text{ As, } q = 1 - p \right]$
$\Rightarrow 10p = 1$
$\therefore p = \frac{1}{10}$

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

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
Very Short Answers | Q 12 | Page 27