We have two six-sided dice (faces numbered 1 through 6) and two tetrahedral dice (faces numbered 1 through 4). Someone selects two of them and throws each once. Then they tell us the sum of the eyes is 7. Estimate which two they selected by using the maximum likelihood principle.
This is a problem on an old probability theory exam. Unfortunately we only ever calculated pretty straightforward examples in class and I have no idea how to tackle this one. However, since the expected value for the sum of the eyes of two six-sided dice is $7$ I guess they likely selected both of these! How can we approach this problem?
Hint:
What is the probability of a sum of $7$ from two six-sided dice?
What is the probability of a sum of $7$ from two four-sided dice?