Probability Calculator
Find the probability of two independent events both happening, or at least one happening.
The formulas (independent events)
P(A and B) = P(A) × P(B) — the chance both independent events occur.
P(A or B) = P(A) + P(B) − P(A and B) — the chance at least one occurs. The overlap is subtracted once so it isn't double-counted.
Worked example
If P(A) = 0.3 and P(B) = 0.4, then P(A and B) = 0.3 × 0.4 = 0.12, and P(A or B) = 0.3 + 0.4 − 0.12 = 0.58.
How percentages and decimals are read
- Each box accepts a probability from 0 to 1, or a percentage from above 1 up to 100.
- Any entry greater than 1 is divided by 100. So 25 is read as 0.25 and 1.5 is read as 0.015, which is 1.5%.
- An entry of exactly 1 stays 1, meaning a certain event, not 1%. To enter one percent, type 0.01.
- Negative numbers and anything above 100 give an error. Fractions such as 1/6 are not accepted; type 0.1667 or 16.67 instead.
- Results are decimals to four places, not percentages, so multiply by 100 to read them as percent.
More worked examples
Entering 25 and 50 is the same as 0.25 and 0.5. Both happen with probability 0.1250, and at least one happens with probability 0.6250.
With 0.5 and 0.5 the figures are 0.2500 and 0.7500. With A certain (1) and B at 0.5, P(A and B) is 0.5000 and P(A or B) is 1.0000, because an event that always happens guarantees the union.
The tool does not show "exactly one" separately, but you can find it by subtracting: for 0.3 and 0.4 that is 0.5800 − 0.1200 = 0.4600.
Scope
Only two events are covered, and both are assumed independent. There is no conditional probability, no three-event version and no complement output, although the chance of an event not happening is simply 1 minus its probability.
Input rules and an example
Probabilities can be typed as decimals or percentages, because any value above 1 is divided by 100. 0.5 and 0.4 give P(A and B) of 0.2000 and P(A or B) of 0.7000. Typing 50 means 50%, and a value over 100 returns "Probabilities must be between 0 and 1 (or 0% and 100%)."
Watch the boundary. A 1 is read as a probability of 1, meaning certain, but 1.2 is read as 1.2%, so 1.2 and 0.4 give 0.0048 and 0.4072 rather than an error. The tool also assumes the two events are independent, so P(A and B) is just the two numbers multiplied, which is wrong when one event affects the other. Results are rounded to four decimals.
Frequently asked questions
What does 'independent events' mean?
Two events are independent if the outcome of one doesn't affect the probability of the other — like two separate coin flips, or drawing a card and rolling a die.
Does this work for dependent events?
No. This calculator assumes independence. For dependent events (like drawing two cards from a deck without replacement), the second probability changes based on the first outcome, which needs a different calculation.
Is 1 read as 1% or as 100%?
As 100%, a probability of 1. Only values above 1 are treated as percentages, so use 0.01 for one percent.
Why does it reject 1/6?
The boxes take plain numbers only. Enter the decimal 0.1667, or 16.67 as a percentage.
How do I find the chance that exactly one of the two happens?
Take the P(A or B) result and subtract P(A and B). For 0.3 and 0.4 the answer is 0.58 minus 0.12, or 0.46.