Solving Probability Problems: Normal Distributions and the Chance of B < A

[Marije]

Probability question

I can't figure out how to solve this problem.

Given are two normal distributions, A: Norm(12; 0,4) and B: Norm(13; 0,9).
If we pick one from A and one from B what's the chance B < A?
I don't know how to do this because we haven't learned a formula or anything for the graphs. I think what they're asking for is to calculate the area I coloured in this picture:
http://img211.imageshack.us/img211/1692/kansberekeningsk5.jpg
Sorry for the crappy drawing skills. I hope you understand the idea anyway.
Is there any way to calculate it? ;x I'm lost.

Oops sorry I think I posted this in the wrong section... Sorry, I'm new here. I'm not sure if this should go here or in the homework section, since there are more questions like mine in this forum but it's homework so I don't know, sorry.

 

[mathman]

Have you learned how to get the distribution for the sum (or difference) of two independent random variables, particularly of normal variables? If so, let x be chosen from A, y chosen from B, and let z=x-y. z will be normally distributed and you need to get prob (z<0).