conditional probability

Topics

• probability

Conditional probability describes the likelihood of an event $A$ occurring, given that another event $B$ has already occurred.

$$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

Where:

• $P(A\mid B)$ is the conditional probability of $A$ given $B$
• $P(A\cap B)$ is the joint probability of both $A$ and $B$ occurring
• $P(B)$ is the probability of $B$ occurring

Conditional probability is crucial in bayesian inference and markov models. It allows updating probabilities based on new evidence.

Above illustration shows how $P(B\mid A)\ne P(A\mid B)$.