I just came across a blog post. I believe the answer is a correct approximation:
http://tastytradenetwork.squarespace.com/tt/blog/probability-of-touching-both-sides
I modified the question in the post to: What is the combined probability of the stock moving up to touch the short call strike but not touching the short put strike price of the short strangle?
**Same delta values of 0.3 for the call and 0.3 for the put. Assume symmetric random walk.