Probability Calculator
Compute the probability of single events, unions, intersections and complements. Choose whether events are independent, mutually exclusive or general, enter the relevant probabilities, and the calculator returns the combined probability with the formula used.
Choose a probability type
Choose a mode, enter values, and press Calculate.
Probability basics
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). It can be expressed as a fraction, a decimal or a percentage.
P(event) = favourable outcomes / total outcomes
Key rules
- Complement:
P(not A) = 1 − P(A) - Independent intersection:
P(A and B) = P(A) × P(B) - Mutually exclusive union:
P(A or B) = P(A) + P(B) - General union:
P(A or B) = P(A) + P(B) − P(A and B) - Neither:
P(not A and not B) = 1 − P(A or B)
Worked examples
Example 1 — Two coin flips (independent)
Probability of heads on both flips, where P(H) = 0.5.
0.5 × 0.5 = 0.25 → 25%.
P(HH) = 0.25
Example 2 — Rolling a die (mutually exclusive)
Probability of rolling a 1 or a 2.
1/6 + 1/6 = 2/6 = 1/3 ≈ 0.333.
P(1 or 2) ≈ 0.333
Example 3 — Complement
If P(rain) = 0.3, what is P(no rain)?
1 − 0.3 = 0.7.
P(no rain) = 0.7
Example 4 — At least one of two events
P(A) = 0.4, P(B) = 0.3, independent. What is P(A or B)?
P(A and B) = 0.12. P(A or B) = 0.4 + 0.3 − 0.12 = 0.58.
P(A or B) = 0.58
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Frequently asked questions
Independent events do not influence each other (two separate coin flips). Mutually exclusive events cannot both occur at the same time (rolling a 1 and a 2 on the same die roll).
No. Probability is always between 0 and 1 inclusive (0% to 100%). If your calculation produces a value outside that range, check the inputs — usually P(A and B) was entered as too large, or a decimal was typed as a percentage.
Yes. Type the fraction directly (e.g. 1/4) and the calculator evaluates it. You can also enter decimals (0.25) or percentages (25%).