Last Updated on March 2, 2026 | 1 : 44 pm by Anas Brittany
Use this conditional probability calculator to find the probability of event A happening given that event B has already happened. Conditional probability is written as P(A|B) and is widely used in statistics, data science, risk analysis, and everyday decision-making.
Conditional Probability Calculator
What Is Conditional Probability?
Conditional probability is the probability of an event happening when you already know another event has occurred. It is written as P(A|B), which means “the probability of A given B.”
This concept is used whenever new information changes the likelihood of an outcome.
Conditional Probability Formula
The standard formula is:
P(A|B) = P(A ∩ B) / P(B)
Where:
- P(A|B) = probability A happens given B happened
- P(A ∩ B) = probability that both A and B happen
- P(B) = probability that B happens
This formula works only when P(B) > 0.
How to Find Conditional Probability
To calculate conditional probability:
- Find the probability that both events happen (A and B)
- Divide that value by the probability that B happens
This gives you the probability of A restricted to only situations where B is already true.
Conditional Probability Example
If:
- P(B) = 0.25
- P(A ∩ B) = 0.10
Then:
P(A|B) = 0.10 ÷ 0.25 = 0.40
So the probability of A happening given B has happened is 0.40 (40%).
Conditional Probability vs Independent Events
If A and B are independent, then knowing B happened does not change the probability of A.
That means:
P(A|B) = P(A)
If your calculated conditional probability is very different from P(A), the events are likely dependent.
Frequently Asked Questions
What does P(A ∩ B) mean?
P(A ∩ B) means the probability that both A and B occur at the same time.
Can conditional probability be greater than 1?
No. Conditional probability must always be between 0 and 1 (or 0% and 100%).
What happens if P(B) = 0?
Conditional probability is undefined because the formula divides by P(B).
Brittany Anas is a freelance lifestyle journalist and editorial writer with experience covering culture, food, lifestyle, entertainment, and evergreen guides for digital publications. Her writing focuses on clear research, approachable storytelling, and practical ideas designed for everyday readers.
On Fiestasline, Brittany contributes editorial content across lifestyle, ideas, food & drink, culture, and curated guides, helping readers discover inspiration that’s timely, accessible, and easy to enjoy.
