#philosophy 

$$\LARGE P(B|A)=\frac{P(B)\cdot P(A|B)}{P(A)}$$

Suppose that we have some hypothesis, and a piece of evidence for it.
Then:

$$\LARGE P(h|e)=\frac{P(h)\cdot P(e|h)}{P(e)}$$

$\LARGE P(h|e)$ is the **posterior probability of the hypothesis** - after the evidence comes in
$\LARGE P(h)$ is the **prior or antecedent probability of the hypothesis** - how likely the hypothesis from the word go
$\LARGE P(e|h)$ is **the probability of the evidence, given h**. Measure of the **fit** between the hypothesis and the evidence. - how well does the evidence accord with the hypothesis
$\LARGE P(e)$ is the **prior or antecedent probability of the evidence** itself. - how likely is the evidence from the word go

Example:
![[Pasted image 20240908152421.png]]