Probability Calculator
Enter the probability of two independent events, A and B, to find the probability of both happening, either happening, or A not happening.
This calculator assumes events A and B are independent — the outcome of one doesn't affect the other.
How these probability rules work
For independent events, the probability both A and B happen is the product of their individual probabilities: P(A and B) = P(A) × P(B). This works because independence means knowing A happened tells you nothing about B's chances.
The probability that A or B (or both) happens is P(A or B) = P(A) + P(B) − P(A and B) — subtracting the overlap avoids double-counting the outcomes where both occur. The probability A doesn't happen is simply 1 − P(A), since "A happens" and "A doesn't happen" cover all possibilities.
Frequently asked questions
What does it mean for two events to be independent?
Two events are independent if the occurrence of one doesn't change the probability of the other — like flipping a coin twice, where the first flip's result has no effect on the second.
Why do you subtract P(A and B) when finding P(A or B)?
Without subtracting, the outcomes where both A and B happen would be counted twice — once in P(A) and once in P(B) — so subtracting P(A and B) corrects for that double-counting.
Does this work for dependent events?
No — these formulas assume independence. For dependent events (where one outcome affects the other's probability), you'd need conditional probabilities, which this calculator doesn't handle.