[eatkinson]

This isn't really sound reasoning, for reasons mentioned elsewhere and because of the following.

You need to know that the probability of acceptance is conditionally independent of the "type" of the applicant given the success of the applicant.

For example, consider the following hypothesis for the First Round data: women are more honest than men. A woman presenting a bad idea to a VC will be rejected whereas a man may be able to weasel his way into getting funding. This will make men have a lower success rate, and correspondingly women will have a higher success rate.

However, this isn't really the same thing as having an across-the-board hidden bias against women.