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.
Enter probabilities in the order of A1B1, A1B2, A2B1, A2B2, ...
Conditional Probabilities P(A|B):
P(A|B) =
Visualization Table
| A \ B | |
|---|---|
Calculation Steps
For Event A = and Event B = :
- Joint Probability P( and ) =
- Probability of Event B, P() = (Sum of joint probabilities for all A values with this B)
- Conditional Probability P( | ) = P( and ) / P() =
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.