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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

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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.

 
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APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
MCQ | Q: 23 | Page no. 29
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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.
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