Tyler rolls two, fair, six-sided dice, one die is red and one is blue. Calling the value of the red die R and the sum of the dice S, he then solves the equation $x^2+Rx=1$ and choose the greater solution is S is even and the lesser solution if S is odd.
What is the expected value of the solution he finds?
(I.E. The average value if he does this repeatedly.)
(I feel that the problem doesn't provide enough information; however, please correct me if I am wrong.)
There is plenty of information. If I told you that $R=1$ and $S$ is even, could you find the number you choose? It is a quadratic equation. There are twelve cases, six choices for $R$ and even/odd for $S$, all equally probable. The pedestrian approach is to make a table of all twelve cases, add up the numbers you get, and divide by $12$. This proves there is enough information.
There is an easier way. Do you know something about the sum of the roots of a quadratic equation?