Let's say I roll a $6$-sided die and a $10$-sided die. Now, if I am going to pay the sum of the two rolls, how much will I pay on average?
The average sum of a single $6$-sided die would be $3.5$ --> $\frac{1+2+3+4+5+6}{6}$
The average sum of a single $10$-sided die would be $5.5$ --> $\frac{10+9+8+7+6+5+4+3+2+1}{10}$
So am I correct if I say that on average I would pay $4.5$ --> $\frac{5.5+3.5}{2}$ ?