Answer
10.5
Work Step by Step
Let $S$ be the random variable denoting the sum of the numbers when a fair dice is rolled. Let $s1$, $s2$ and $s3$ denote the corresponding sums for the three dice. We have $S=s1+s2+s3$.
$E(S)=E(s1+s2+s3)=E(s1)+E(s2)+E(s3)$.
The expectation of the sum is the sum of the expectation values of the three dices. but since they are all fair dice, they have the same expectation values. Hence $E(S)=3E(s1)$.
The outcomes for a single fair die are $1,2,3,4,5,6$ each with probability $\frac{1}{6}$.
$E(X)=\sum _iXP(X=i)$ for $i=1$ to $6$.
$E(s1)=\frac{(1+2+3+4+5+6)}{6}=3.5$
Hence, $E(S)=3 \times 3.5=10.5$.
