Question

A die is tossed thrice. A success is getting $1$ or $6$ on a toss. The mean and the variance of number of successes

• A. $\mu =1,{\sigma }^2=2/3$
• B. $\mu =2/3,{\sigma }^2=1$
• C. $\mu =2,{\sigma }^2=2/3$
• D. None of these

Answer 1

Answer: (A)

$n=3,p=\frac{2}{6}=\frac{1}{3}$
mean $=np=3\times \frac{1}{3}=1$
variance ${\sigma }^2=npq=\sqrt{3\times \frac{1}{3}\times \frac{2}{3}}$
$=3\times \frac{1}{3}\times \frac{2}{3}$
${\sigma }^2=\frac{2}{3}$