Probability Calculator

Combine the probabilities of two independent events. Enter the chance of each, and the calculator shows the probability of both, either, neither, and exactly one happening.

P(A and B) — both 0%
P(A or B) — either 0%
P(neither) 0%
Exactly one 0%

Combining two independent events

When two events don't affect each other, their combined probabilities follow simple rules:

P(A and B) = P(A) × P(B)

P(A or B) = P(A) + P(B) − P(A and B)

P(neither) = (1 − P(A)) × (1 − P(B))

For two coin-flip-like events at 50% each: both is 25%, either is 75%, neither is 25%, and exactly one is 50%.

Why subtract the overlap?

Adding P(A) and P(B) alone counts the "both happen" case twice. Subtracting P(A and B) corrects for that double-count, which is why "either" isn't simply the sum of the two probabilities.

A note on independence

These formulas assume the events are independent. If one event changes the odds of the other, you'd need conditional probability instead. For counting arrangements and selections, see the permutation & combination calculator.

Frequently asked questions

How do you calculate the probability of two events both happening?

For two independent events, multiply their probabilities: P(A and B) = P(A) × P(B). If each has a 50% chance, both happening is 0.5 × 0.5 = 0.25, or 25%. Independent means one event does not affect the other.

How do you find the probability of either event happening?

Add the two probabilities and subtract the overlap so it is not double-counted: P(A or B) = P(A) + P(B) − P(A and B). For two 50% events that is 0.5 + 0.5 − 0.25 = 0.75, or 75%.

What does "independent events" mean?

Two events are independent when the outcome of one has no effect on the other — like two separate coin flips. This calculator assumes independence. If the events influence each other, you would need conditional probabilities instead.

How do I find the probability that neither event happens?

Multiply the chances of each not happening: P(neither) = (1 − P(A)) × (1 − P(B)). For two 50% events that is 0.5 × 0.5 = 0.25. Neither happening is the complement of "at least one" happening.

Can probabilities be greater than 100%?

No. A probability ranges from 0 (impossible) to 1, or 0% to 100% (certain). If you enter a value above 100%, it is not a valid probability, so the calculator treats inputs as percentages between 0 and 100.

Disclaimer: Results assume independent events and inputs between 0% and 100%. Provided for educational purposes.