Mathematical Expectation

Question

A game is played wherein two fair dice are rolled and the sum of the two top faces is calculated. If the sum is 7, the player wins \$1.50. If the sum is not 7 or 2, then the player loses \$1.00. What is the mathematical expectation of a single roll.

I feel as if this problem is missing information when the dice add up to 2. So far the mathematical expectation is $\left(\frac{6}{36}\right)(1.5)+\left(\frac{29}{36}\right)(-1)$ What happens to the $\frac{1}{36}$ chance for a sum of 2?

Answer 1

There is missing information about the outcome associated with $2$. Given that no information is provided, one might argue that the most sensible interpretation to fill the gap is that the payoff from the outcome $2$ is zero. Under this interpretation, the expectation in your question is the answer.

Answer 2

As the question is written, I would assume no money changes hands on a $2$ and your answer is correct. If you want you could show another term $\left(\frac{1}{36}\right)(0)$ to show you thought about it.