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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Probability

NDA 2010 · Mathematics · Probability

The mean and variance of a binomial distribution are 8 and 4...

The mean and variance of a binomial distribution are 8 and 4 respectively. What is P(X=1)\mathrm{P}(\mathrm{X}=1) equal to?

Options

  1. A1212\frac{1}{2^{12}}
  2. B128\frac{1}{2^8}
  3. C126\frac{1}{2^6}
  4. D124\frac{1}{2^4}

Correct answer

A. 1212\frac{1}{2^{12}}

Step-by-step solution

np=8,npq=4q=12, so p=12np=8,n×12=8⇒n=16\begin{aligned} & n p=8, \quad n p q=4 \\ & q=\frac{1}{2}, \text{ so } p=\frac{1}{2} \\ & n p=8, n \times \frac{1}{2}=8 \Rightarrow n=16\end{aligned}∴p(X=1)=16C1(12)15(12)1=16×(12)16=1212\begin{aligned} & \therefore p(\mathrm{X}=1)={ }^{16} \mathrm{C}_1\left(\frac{1}{2}\right)^{15}\left(\frac{1}{2}\right)^1 \\ & =16 \times\left(\frac{1}{2}\right)^{16}=\frac{1}{2^{12}}\end{aligned}$
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