Probability distribution of dice

Question

If 5 true dice are thrown once, determine the probability of getting 0,1,2,3,4,5 sixes. Find the mean and variance of the probability distribution so obtained

Answer 1

Taking into account, that the dice is fair we have a Bernoulli experiment.

When $X$ counts the number of sixes, with $p=1/6$ and $q=5/6$, the probability for exactly $k$ sixes in 5 throws is given by:

$P(X=k)=\binom{5}{k}p^k\cdot q^{5-k}$

The mean $\mathbb{E}(X)$ of a bernoulli experiment is $p$.

The variance $\operatorname{Var}(X)$ is given by $pq$.