Calculating Probability of Score Comparison between Two Distributions

[cstoos]

Forgive me if this is a silly question, but here goes:

Say you have two unrelated distributions (A and B) with known means and standard deviations. How would you determine the probability of any single value of A being greater than any single value of B?

The easiest example I can come up with for clarification would be something like this:

Over 1000 games baseball team A scores: μ_A=5 runs, σ_A=1 runs per game.
Over 1000 games baseball team B scores: μ_B=4 runs, σ_B=2 runs per game.

What is the probability on any given day that Team A outscored Team B? Sorry if this example seems elementary, but I am far from a statistician. Thanks for the help.

 

[mathman]

Direct method: Let C = A-B (there are standard methods to get the distribution function for C, given the distribution functions for A and B). Then compute P(C > 0).