Random inequalities VIII: folded normals

Someone who ran into my previous posts on random inequalities asked me how to compute random inequalities for folded normals. (A folded normal random variable is the absolute value of a normal random variable.) So the question is how to compute

Pr(|X| > |Y|)

where X and Y are normally distributed. Here’s my reply as a short tech report: Inequality probabilities for folded normal random variables.

Previous posts in this series:

Analytical results
Numerical results
Cauchy distributions
Beta distributions
Gamma distributions
Three or more random variables