What is Conditional Probability?
Conditional probability calculates the likelihood of event A occurring given that event B has already occurred. It's essential in statistics, machine learning, and risk assessment. Understanding how to calculate conditional probability helps in predicting outcomes based on prior information, analyzing relationships between events, and making data-driven decisions in fields like finance, healthcare, and artificial intelligence.
Calculator
Formula
Conditional Probability Formula: P(A|B) = P(A∩B) / P(B)
How to Use
1. Enter probability of both events occurring (P(A∩B)) between 0-1
2. Enter probability of event B (P(B)) between 0-1
3. Click Calculate to get P(A|B)
4. Results show probability of A given B has occurred
Note: Values must be between 0 and 1
Derivation Process
The conditional probability formula derives from Bayes' theorem. By restricting the sample space to event B, we consider only outcomes where B occurs. The probability of A within this restricted space equals the probability of both events occurring divided by the probability of B. This normalization ensures the total probability in the restricted space remains 1.