bayes theorem

$$\begin{array}{c}P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}\end{array}$$

To find the probability of event (A) occurring given event (B) has occurred, we multiply the likelihood of event (B) given event (A) by the prior probability of event (A) and divide by the marginal probability of event (B)¹.

Note that the marginal probability (P(B)) acts as a normalization constant, ensuring that the posterior probabilities sum to 1, and it is computed as the sum of probabilities across all possible causes of (B).

1. Bayes' theorem