Probability Calculator

How the probability calculator works

Enter the chance of event A and event B and the calculator returns the probability of A and B, A or B, neither, exactly one, and the chance that A happens at least once or every time in n repeats. It assumes the events are independent and shows the working for A and B.

Worked example

Let P(A) = 0.3 and P(B) = 0.5. Both happen with probability 0.3 × 0.5 = 0.15. Either happens with probability 0.3 + 0.5 − 0.15 = 0.65. Neither happens with probability 0.7 × 0.5 = 0.35, and 0.65 + 0.35 = 1 confirms the numbers add up.

“At least once” in repeated tries

The quickest way to find the chance of at least one success is to subtract the chance of none from 1. If A has probability 0.3 and you try three times, the chance of never is 0.7³ = 0.343, so at least once is 1 − 0.343 = 0.657, or 65.7 %.

Independent versus dependent events

Events are independent when one outcome does not change the chance of the other, like two separate coin flips. If you draw two cards from a deck without putting the first back, the events are dependent and multiplying the original probabilities gives the wrong answer. Two aces in a row is 4/52 × 3/51 = 1/221, not 4/52 × 4/52 = 1/169; use conditional probability instead.

• Probabilities are always between 0 and 1.
• P(A or B) can never be smaller than the larger of P(A) and P(B).
• P(A and B) can never be larger than the smaller of the two.

Frequently asked questions

See the Factoring Calculator home page for more step-by-step tools.