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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Probability

NDA 2019 · Mathematics · Probability

In eight throws of a die, 5 or 6 is considered a success. The mean...

In eight throws of a die, 5 or 6 is considered a success. The mean and standard deviation of total number of successes is respectively given by

Options

  1. A83,169\frac{8}{3}, \frac{16}{9}
  2. B83,43\frac{8}{3}, \frac{4}{3}
  3. C43,43\frac{4}{3}, \frac{4}{3}
  4. D43,169\frac{4}{3}, \frac{16}{9}

Correct answer

B. 83,43\frac{8}{3}, \frac{4}{3}

Step-by-step solution

5 or 6 is success ∴p=26=13∴q=1−13=23n=8\begin{aligned} & \therefore p=\frac{2}{6}=\frac{1}{3} \\ & \therefore q=1-\frac{1}{3}=\frac{2}{3} \\ & \mathrm{n}=8\end{aligned}\thereforeMeanMean=\mathrm{np}=8(13)=83\left(\frac{1}{3}\right)=\frac{8}{3} Standard deviation $=\sqrt{n p q}=\sqrt{8\left(\frac{1}{3}\right)\left(\frac{2}{3}\right)}=\sqrt{\frac{16}{9}}=\frac{4}{3}
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