Conditional Probability Calculator
Calculate P(A given B) and P(B given A) with clear formulas, examples, and step-by-step probability explanations.
Calculator
Enter probabilities as decimals, such as 0.25 for 25%.
What this calculator teaches
Conditional probability measures the chance that event A happens after you already know event B happened. It is one of the most important ideas in high-school probability, statistics, data science, medical testing, and risk analysis.
The key idea is that the sample space becomes smaller. Instead of looking at all outcomes, you look only at the outcomes where B occurred.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| Conditional probability | P(A|B)=P(A∩B)/P(B) | The probability of A given B equals the overlap divided by the probability of B. |
| Reverse condition | P(B|A)=P(A∩B)/P(A) | The probability of B given A may be different from P(A|B). |
Step-by-Step Examples
- Suppose P(sports and music) = 0.18.
- Suppose P(music) = 0.30.
- Then P(sports | music) = 0.18 / 0.30.
- If P(sports) = 0.45, then P(music | sports) = 0.18 / 0.45.
- This uses the same overlap but a different denominator.
Where students use this
Common Mistakes to Avoid
For P(A|B), divide by P(B), not by P(A).
These are usually different because the given information changes.
Use 0.30 for 30%, not 30.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This formula summarizes data, models uncertainty or supports inference about a population or random process. Assumption: The sampling design and distribution assumptions must match the data. Independence, sample size, outliers and measurement quality can materially affect interpretation.