A prime number, by definition, has only one factor greater than one--itself. Thus, we can eliminate several possible values of mn. In fact, when both of the random chosen numbers are greater than 1, the result cannot be prime. For instance, (2)(3) = 6, which is not prime.

The only remaining possibilities are those in which one of the chosen numbers is 1:

m - n
1 - 1
1 - 3
1 - 5
1 - 7
2 - 1
3 - 1
4 - 1

However, some of those products are not prime. 1 and 4 are not prime, leaving us with only 5 of those 7 possibilities. 5, then, is the numerator of the fraction: 5 is the number of desired outcomes.

The number of possible outcomes is the number of possible pairings of m and n. That we can find by multiplying the number of possible m's by the number of possible n's. The result is 16, so the answer is 5/16, choice (C).