Question

A die is thrown twice. If getting a number greater than four on the die is considered a success, then the variance of the probability distribution of the number of successes is

• A. $\frac{2}{3}$
• B. $\frac{1}{3}$
• C. $\frac{4}{9}$
• D. $\frac{8}{9}$

Answer 1

Answer: (C)

$\frac{4}{9}$

Answer 2

On throwing a dice a number greater than four on the die is $5,6$.
$\therefore$ Probability of success $(p)=\frac{2}{6}=\frac{1}{3}$
$\therefore q=1-p=1-\frac{1}{3}=\frac{2}{3}$
Now, variance of probability distribution
$=n p q (\because n=2)$
$=2 \times \frac{1}{3} \times \frac{2}{3}=\frac{4}{9}$