\[PAB=\frac{PABi}{PB}\]
Variables
PABconditional probability of A given B
PABijoint probability of A and B
PBprobability of event B
Description
What is this formula?
Conditional Probability calculates the probability that an event A occurs given that another event B has already occurred.
It is one of the fundamental concepts of probability theory and serves as the basis for Bayes' Theorem, statistical inference, machine learning, and risk analysis.
When to use it
Use this formula when the occurrence of one event provides information about the likelihood of another event.
Example
Suppose:
Joint Probability of A and B:
PABi = 0.12
Probability of B:
PB = 0.30
Formula:
PAB=PABi/PB
Substitution:
PAB=0.12/0.30
PAB=0.40
Result:
Conditional Probability = 40%
Applications
Econometrics
Risk analysis
Insurance modeling
Machine learning
Statistical inference
Financial forecasting
Decision analysis