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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Probability

NDA 2023 · Mathematics · Probability

In a Binomial distribution B(n, p), n=6 and 9 P(X=4)=P(X=2) . What...

In a Binomial distribution B(n,p),n=6B(n, p), n=6 and 9P(X=4)=P(X=2)9 P(X=4)=\mathrm{P}(\mathrm{X}=2). What is p equal to?

Options

  1. A14\frac{1}{4}
  2. B12\frac{1}{2}
  3. C34\frac{3}{4}
  4. D45\frac{4}{5}

Correct answer

A. 14\frac{1}{4}

Step-by-step solution

Since, given n=6\mathrm{n}=69P(x=4)=P(x=2)⇒96C4P4q2=6C2P2q4⇒p2q2=19⇒pq=13⇒q=3p\begin{aligned} & & 9 \mathrm{P}(\mathrm{x}=4)=\mathrm{P}(\mathrm{x}=2) \\ & \Rightarrow 9^6 \mathrm{C}_4 \mathrm{P}^4 \mathrm{q}^2={ }^6 \mathrm{C}_2 \mathrm{P}^2 \mathrm{q}^4 \\ & \Rightarrow \frac{\mathrm{p}^2}{\mathrm{q}^2}=\frac{1}{9} \Rightarrow \frac{\mathrm{p}}{\mathrm{q}}=\frac{1}{3} \Rightarrow \mathrm{q}=3 \mathrm{p} \end{aligned}$SinceSincep+q=1 \Rightarrow p=\frac{1}{4}$
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