# For a Binomial Variate X, If N = 3 and P (X = 1) = 8 P (X = 3), Then P = (A) 4/5 (B) 1/5 (C) 1/3 (D) 2/3 - Mathematics

MCQ

For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =

#### Options

• 4/5

• 1/5

• 1/3

• 2/3

• None of these

#### Solution

n =3

$P(X = 1) = 8 P(X = 3) (\text{ Given } )$
$\text{ The distribution is given by }$
$P(X = r) =^{3}{}{C}_r \left( p \right)^r \left( q \right)^{3 - r}$
$P(X = 1) =^{3}{}{C}_1 \left( p \right)^1 \left( q \right)^2 \text{ and } P(X = 3) =^{3}{}{C}_3 \left( p \right)^3 \left( q \right)^0$
$\Rightarrow 3p q^2 = 8 p^3$
$\Rightarrow 8 p^2 = 3 q^2$
$\Rightarrow 8 p^2 = 3(1 - p )^2$
$\Rightarrow 8 p^2 = 3 - 6p + 3 p^2$
$\Rightarrow 5 p^2 + 6p - 3 = 0$
$\Rightarrow p = \frac{- 6 \pm \sqrt{96}}{10}$

Hence , it does not match any of the answer choices.

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

RD Sharma Class 12 Maths
Chapter 33 Binomial Distribution
MCQ | Q 23 | Page 29