#### Question

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.

Is there an error in this question or solution?

Advertisement

Advertisement

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 Concept: Bernoulli Trials and Binomial Distribution.

Advertisement