How to calculate a simple Bayesian posterior probability tree

We use the example of successful startups that were founded by female founders.*

First start with a tree from both sides of the prior probabilities. P(FE), P(S) is the prior probability of event FE and S to occur. 

Equate both conditional probabilities P(FE|S) and P(S|FE) because P(S∩FE) = P(FE∩S)

P(FE|S) is the likelihood, or the probability of a female start-up founder given a successful start-up

Ultimately, we derive P(S|FE) which is the posterior probability or the probability of a startup success to occur given it was found by a female founder 

Solution: P(S|FE), the probability of a start-up success given that it was founded by a female founder is 0,25%. 

Hint: It is best to memorize the following formula 

* This is by no means an anti-feministic post