Probability Calculator

Find the probability of a single event, or combine two independent events using AND / OR logic.

Probability Calculator

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Event A: favorable outcomes

Event A: total outcomes

Combine with a second event?

Probability of Event A

16.67%

AND / OR combinations assume the two events are independent of each other.

The formulas

Single event: P(A) = favorable outcomes / total outcomes Independent AND: P(A and B) = P(A) x P(B) Independent OR: P(A or B) = P(A) + P(B) - P(A) x P(B)

Example

Rolling a 6 on a die: P = 1/6 ≈ 16.67%. Rolling a 6 on one die AND flipping heads on a coin: 1/6 x 1/2 ≈ 8.33%.

Step-by-step guide

Enter the favorable and total outcomes for Event A.
Choose whether to combine with a second event, and if so, AND (both happen) or OR (at least one happens).
Read the resulting probability as a percentage.

Common mistakes

Adding probabilities for AND instead of multiplying - "and" means both things must happen, which is generally less likely than either alone, so the probabilities multiply.

Applying this independent-events formula to events that actually affect each other (like drawing cards without replacement) - that situation needs conditional probability instead.

Frequently asked questions

What does "independent" mean here?

Independent means the outcome of one event doesn't affect the other - like a coin flip and a die roll. If one event changes the odds of the other (like drawing cards without putting them back), these formulas don't directly apply.

Why subtract P(A) x P(B) in the OR formula?

Without subtracting, the overlap where both A and B happen would be counted twice. Subtracting P(A and B) corrects for that double-counting.

Can probability be over 100%?

No - a valid probability is always between 0% and 100%. If your inputs give something outside that range, double-check that "favorable outcomes" doesn't exceed "total outcomes."

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