Probability Calculator
Calculate probabilities of single and multiple events.
Both occur — P(A and B)
15.00%
assuming independence
Either — P(A or B)
65.00%
Neither
35.00%
Exactly one
50.00%
Not A
70.00%
The two master rules
For independent events, 'and' multiplies: P(A)×P(B). 'Or' adds but removes the double-counted overlap: P(A)+P(B)−P(A)P(B). Everything here derives from those two rules plus complements (P(not A) = 1 − P(A)).
Independence is an assumption
These formulas require that A doesn't influence B. Rain and umbrella-carrying aren't independent; coin flips are. When events are linked, you need conditional probability — P(A and B) = P(A)×P(B given A) — and the numbers can shift dramatically.
Frequently asked questions
- How does the Probability Calculator work?
- Calculate probabilities of single and multiple events.
- Is the Probability Calculator free to use?
- Yes. The Probability Calculator is completely free, runs entirely in your browser, and requires no account or sign-up. Your inputs never leave your device.
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