A release-checked easy problem for training Expected Value/LOTUS, Dice.
Question
Alan has two 6-sided dice. One of the dice is a standard fair 6-sided die with the values $1-6$ on the sides. Alan does not know the values on the other die. Note that the values on this other die do not necessarily need to be $1-6$ and can also potentially be repeated. Whenever Alan tosses both dice, each of the integer sums $1-12$, inclusive of both, are equally likely. What is the sum of the values on the sides of the die Alan doesn't know?
Practice focus
This Probability problem is tagged Expected Value/LOTUS, Dice. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.