Probability Calculator
Enter the chance of each of two independent events. You get both, either, neither and exactly one, plus what happens if you repeat the first event many times.
How the math works
For independent events, both happening is P(A) x P(B). Either happening is P(A) + P(B) - P(A and B), because otherwise the overlap gets counted twice. Neither is (1 - P(A)) x (1 - P(B)). At least once in n tries is 1 - (1 - P(A))^n, which is far easier than adding up all the ways it could happen.
Common questions
- What does independent mean?
- That one event does not affect the other. Two coin flips are independent. Drawing two cards without replacing the first is not, because the first draw changes the deck - this page does not handle that case.
- If something has a 1 in 100 chance, is it certain in 100 tries?
- No. It is about 63 percent. The chance of it never happening is 0.99 to the power of 100, which is roughly 37 percent. Set A to 1 percent and 100 trials above to see it.
- Why subtract when working out "either"?
- Because the case where both happen sits in both lists. Adding the two chances counts it twice, so it gets subtracted once to put it right.
- What are the odds of rolling a six twice in a row?
- Each roll is 1 in 6, about 16.67 percent. Both is 16.67 percent squared, which is about 2.78 percent, or 1 in 36.
- Does the last result change the next one?
- Not for independent events. A coin that has landed heads five times still has a 50 percent chance of heads next. Believing otherwise is the fallacy that gives the gambler false hope.