# Bayes Theorem

- You have a hypothesis
- You have some information
- You want to know if the hypothesis is true given the info

If you want to know the probability of something occurring given two populations, this is what Bayes is for. It is all about a proportion of a population.

The way I think about it:

$$\frac{POP(1)}{POP(1) + POP(2)}$$

More formally:

$$\frac{P(H)P(E|H)}{P(H)P(E|H) + P(\neg H)P(E|\neg H)}$$

- Reads: Probability of the hypothesis times the probability of the evidence given the hypothesis divided by the probability of the hypothesis times the probability of the evidence given the hypothesis plus the probability of of not hypothesis (that the hypothesis is NOT true) times probability of the evidence given that the hypothesis is not true. Phew.

...and more succinctly

$$\frac{P(H)P(E|H)}{P(E)}$$

- Reads: Probability of the hypothesis times the probability of the evidence given the hypothesis divided by the probability of the evidence

...and even more succinctly

`P(H|E)`

= probability of the hypothesis given the evidence.

##### Source:

- Me