Given the E[X] of a discrete uniform random variable...

Given the E[X] of a discrete uniform random variable...

The expected value of a discrete uniform random variable U is 6.5.
a) Find P(U=3).
b) Find the variance of U.
Discrete uniform variables have the following characteristics:
The mean (expected value) is (a+b)/2.
The variance is ((n^2) - 1) / 12.
n = b-a+1.
pmf = 1/n.
My work:
So, I need to find the PMF where U=3. To do that I need to find n. Since I
only have the mean, it follows 6.5 = (a+b)/2. But, I know neither a or b,
so how do I solve? Should my final answer have a variable in it? Is there
another way to figure this out?
wikipedia - uniform discrete distribution