Probability Calculator
Choose between a single event's probability, or the combined probability of two independent events happening together (AND) or either happening (OR).
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
- For a single event, divide the number of favorable outcomes by the total possible outcomes.
- For two independent events happening together (AND), multiply their individual probabilities.
- 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%.