Statistics

Probability Calculator

Choose between a single event's probability, or the combined probability of two independent events happening together (AND) or either happening (OR).

What are you calculating?

Probability
Enter values to calculate.

How the Probability formula works

Three probability formulas:

Single event: P = Favorable outcomes / Total outcomes
AND (independent): P(A and B) = P(A) × P(B)
OR (independent):  P(A or B) = P(A) + P(B) − P(A) × P(B)

Step-by-step calculation

  1. For a single event, divide the number of favorable outcomes by the total possible outcomes.
  2. For two independent events happening together (AND), multiply their individual probabilities.
  3. For either of two independent events happening (OR), add their probabilities and subtract the probability of both happening together, to avoid double-counting.

Worked example

Rolling a die: P(rolling a 4) = 1/6 ≈ 16.7%. Rolling two dice, P(both show a 4) = 1/6 × 1/6 ≈ 2.8%. P(either die shows a 4) = 1/6 + 1/6 − 1/36 ≈ 30.6%.

Frequently asked questions

What does 'independent events' mean?

Independent events don't affect each other's outcome — like separate coin flips or dice rolls. The AND/OR formulas here assume independence; dependent events (where one outcome changes the odds of another) require different formulas.

Can probability be greater than 1 or less than 0?

No — probability is always between 0 (impossible) and 1 (certain), often expressed as a percentage from 0% to 100%.