Question

If two dice are rolled 12 times, obtain the mean and the variance of the distribution of successes, if getting a total greater than 4 is considered a success.

Answer 1

Let X denote the number of successes in 12 trials. Then, X follows binomial distribution with parameters $n=12$

p = Probability of getting a total greater than 4 in a single throw of a pair of dice.

$p=1-\frac{6}{36}=\frac{5}{6}$

$q=1-p=1-\frac{5}{6}=\frac{1}{6}$

Therefore,

Mean = $np=\frac{5}{6}\times 12=10$

And,

Variance = $npq=12\times \frac{5}{6}\times \frac{1}{6}=\frac{5}{3}$.