Conditional Probability Calculator

Easily calculate conditional probability P(A|B) for discrete random variables. Enter event values and joint probabilities to get instant results.

Input Values

Enter comma-separated values for Event A, Event B, and their Joint Probabilities.

Event A Values

Event B Values

Joint Probabilities P(A and B)

Enter probabilities in the order of A1B1, A1B2, A2B1, A2B2, ...

Conditional Probabilities P(A|B):

P(A|B) =

Visualization Table

A \ B

Calculation Steps

Understanding Conditional Probability

Conditional probability is the likelihood of an event occurring given that another event has already happened. It's a fundamental concept in probability theory and statistics.

The formula for conditional probability is:

$$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A \text{ and } B)}{P(B)}$$

Where:

$P(A|B)$ is the conditional probability of event A given event B.
$P(A \cap B)$ or $P(A \text{and} B)$ is the joint probability of both events A and B occurring.
$P(B)$ is the probability of event B occurring.

Conditional probability is widely used in risk assessment, medical diagnosis, and various fields to analyze dependencies between events and make informed decisions based on prior knowledge.