Conditional Probability Calculator
Calculate the probability of event A given event B.
Conditional Probability Formula
P(A|B) = P(A ∩ B) / P(B), provided P(B) is greater than zero.
Understanding Conditional Probability
Conditional probability measures the probability of event A occurring when event B is already known to have occurred. It is written as P(A|B).
Conditional Probability Example
If 30 students play a sport and 12 of those also study music, then the probability of studying music given that a student plays a sport is 12/30 = 0.40.
Why It Matters
Conditional probability is central to Bayes theorem, risk analysis and many real-world decisions where new information changes the relevant probability.
Frequently Asked Questions
Is P(A|B) always equal to P(B|A)?
No. Reversing the condition usually changes the probability.
Can conditional probability exceed 1?
No.
What if A and B are independent?
Then P(A|B) equals P(A).
How Conditional Probability Works
Conditional probability measures the chance that event A occurs when event B is already known to have occurred. It is commonly written as P(A|B) and calculated as P(A∩B) divided by P(B), provided P(B) is greater than zero.
This calculator is useful for statistics exercises, risk analysis, quality control and decision problems where one condition changes the relevant sample space. Enter probabilities using the same scale and verify that intersection probability cannot exceed either individual probability. A result of 0.40 means a 40% chance of A among cases where B is true.
Conditional probability should not automatically be interpreted as causation. The result describes a mathematical relationship between events based on the inputs supplied. When working with measured data, sampling quality and how events are defined can materially affect the interpretation.
Methodology and Practical Limits
Conditional probability P(A|B)=P(A∩B)/P(B) when P(B)>0. It is generally not equal to P(B|A); confusing the two is a common interpretation error, especially in diagnostic and screening examples.