Combine the chances of two events
Given the probability of two independent events A and B, this calculator works out the everyday combinations: both happening, at least one happening, neither, exactly one, and each events complement. Enter each probability as a number from 0 (impossible) to 1 (certain).
The rules it uses
For independent events, P(A and B) = P(A) times P(B). The OR rule is P(A) plus P(B) minus P(A and B), which subtracts the overlap so it is not double counted. The complement P(not A) is simply 1 minus P(A), and neither is P(not A) times P(not B).
The independence assumption
These multiplications assume the events do not influence each other — one coin flip does not change the next. If A and B are linked, the AND rule needs a conditional probability instead, and the figures here will not apply.
Related tools
To count the outcomes behind a probability, use the combinations and permutations calculator; to gauge how extreme a value is, the z-score calculator.
Worked example
With P(A) = 0.5 and P(B) = 0.3: both is 0.15, either is 0.5 + 0.3 – 0.15 = 0.65, neither is 0.5 times 0.7 = 0.35, and exactly one is 0.5.
FAQ
Can I enter percentages?
Convert first — 30 percent is 0.3. The inputs expect a value between 0 and 1.
What if my events are not independent?
Then P(A and B) is not the simple product; you need the conditional probability P(B given A), and these results overstate or understate the true chance.