Probability Calculator
Calculate probabilities for single events, unions, intersections, conditional probabilities and normal distribution values.
How to use the Probability Calculator
- Enter your inputs into the Probability Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
Key probability formulas
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) · · · P(A | B) = P(A ∩ B) / P(B) · · · For independent events: P(A ∩ B) = P(A) × P(B)
Union is "or" (either or both); intersection is "and" (both). Conditional probability is the probability of A given that B has occurred. Independence means knowing B tells you nothing new about A.
Worked example
Drawing one card from a deck. P(Heart) = 13/52 = 0.25. P(King) = 4/52 ≈ 0.077. P(Heart or King) = 0.25 + 0.077 − 1/52 = 0.308 (subtract the King of Hearts counted twice). P(King given Heart) = 1/13 ≈ 0.077.
Frequently asked questions
What is conditional probability?
The probability of one event given that another has occurred. P(A|B) reads "probability of A given B." It changes the sample space to only the outcomes where B happens.
Are these events independent?
A and B are independent if P(A|B) = P(A) — knowing B doesn't change the probability of A. Many real-world "independent" events are actually slightly dependent in subtle ways.
How does the normal distribution come in?
Many natural quantities (heights, measurement errors) approximately follow a normal distribution. The calculator includes normal CDF and inverse CDF to find probabilities and percentiles.