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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Probability

NDA 2013 · Mathematics · Probability

If X follows a binomial distribution with parameters n=100 and p=1...

If X follows a binomial distribution with parameters n=100n=100 and p=1/3p=1 / 3, then P(X=r)\mathrm{P}(\mathrm{X}=r) is maximum when

Options

  1. Ar=16r=16
  2. Br=32r=32
  3. Cr=33r=33
  4. Dr=34r=34

Correct answer

C. r=33r=33

Step-by-step solution

P(x=r)=(r+1)th term of (q+p)thm=n+11+pq=1011+2=3323\begin{aligned} \mathrm{P}(x=r) & =(r+1)^{\mathrm{th}} \text{ term of }(q+p)^{\mathrm{th}} \\ \mathrm{m} & =\frac{n+1}{1+\frac{p}{q}}=\frac{101}{1+2}=33 \frac{2}{3}\end{aligned}[m]=33t34 will be greatest ∴x=3\begin{aligned} & \quad[\mathrm{m}]=33 \\ & t_{34} \text{ will be greatest } \\ & \therefore \quad x=3\end{aligned}$
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