This probability calculator works out the probability of two independent events happening together, either one happening, neither happening and more. It also handles repeated trials with the binomial distribution, such as the chance of exactly 3 heads in 10 coin flips.
Probability rules for two independent events
| Event | Formula |
|---|---|
| A and B | P(A) × P(B) |
| A or B (at least one) | P(A) + P(B) − P(A) × P(B) |
| Exactly one | P(A) + P(B) − 2 × P(A) × P(B) |
| Neither | (1 − P(A)) × (1 − P(B)) |
| Not A | 1 − P(A) |
Repeated trials (binomial probability)
P(exactly k) = C(n, k) × pk × (1 − p)n − k
n is the number of tries, k the number of successes and p the probability of success on each try. The chance of at least one success in n tries is 1 − (1 − p)n.
Worked example
If the chance of rain on Saturday is 50% and on Sunday 40%, and the two are independent, the chance it rains on both days is 0.5 × 0.4 = 0.2 (20%), and the chance of rain on at least one day is 0.7 (70%). Flipping a fair coin 10 times, the chance of exactly 3 heads is 120 ÷ 1,024 ≈ 11.72%.
Frequently asked questions
How do I enter a percentage?
Divide it by 100. Enter 25% as 0.25 and 3% as 0.03.
What does independent mean?
Two events are independent when one happening does not change the chance of the other, such as two separate coin flips. Drawing cards without putting them back is not independent.
What is the difference between “or” and “exactly one”?
“A or B” includes the case where both happen. “Exactly one” leaves out the case where both happen.
What is the chance of at least one six in four dice rolls?
1 − (5/6)⁴ ≈ 51.77%. Enter 0.166667 as P(A) and 4 as the number of tries.
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Last reviewed: October 2026.