# Probability of touching short call strike and not touching touching short put strike of a short strangle?

I just came across a blog post. I believe the answer is a correct approximation:

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.

If $$A$$ is the event of touching the higher strike (between now and expiry) and $$B$$ is the event of touching the lower strike (and $$B^c$$ is its complement, that is the event of not touching the lower strike), then:
$$P(A\cap B^c) = P(A) - P(A\cap B).$$
They have already estimated POT on the higher (lower) side, $$P(A)$$ ($$P(B)$$), to be twice the probability of stock price at expiry to be less than the higher/lower strike, and POT on both sides, $$P(A\cap B)\approx P(A)\cdot P(B)$$.)