Probability Calculator
Probability measures how likely an event is, from 0 (impossible) to 1 (certain). Once you know the probabilities of simple events you can combine them: the chance something does not happen, that two independent things both happen, that at least one of two happens, or that one happens given the other has. Enter probabilities as decimals, percentages or fractions and see all three forms in the answer.
How to use the probability calculator
- Choose the kind of probability you want.
- Enter P(A) and, where needed, P(B) and P(A and B) as decimals, percentages or fractions.
- Read the result in decimal, percent and fraction form, and check the rule used in the steps.
Formula
- Complement: P(not A) = 1 − P(A)
- Independent AND: P(A and B) = P(A) × P(B)
- OR: P(A or B) = P(A) + P(B) − P(A and B)
- Conditional: P(A | B) = P(A and B) ÷ P(B)
Worked examples
Two sixes
The chance of rolling a six on each of two fair dice is 1/6 × 1/6 = 1/36.
A or B
If P(A) = 0.5, P(B) = 0.3 and they overlap with P(A and B) = 0.1, then P(A or B) = 0.5 + 0.3 − 0.1 = 0.7.
Conditional
If P(A and B) = 0.2 and P(B) = 0.5, then P(A | B) = 0.4.
The rules of probability
Mutually exclusive versus independent
Two events are mutually exclusive if they cannot both happen (rolling a 2 and a 5 on one die). Then P(A and B) = 0. Two events are independent if one does not affect the other (two separate coin flips). Then P(A and B) = P(A) × P(B). They are different ideas: exclusive events with positive probabilities are never independent.
At least one
The chance of at least one success in n independent tries is 1 − (1 − p)ⁿ. If each try succeeds with probability 0.1, five tries give 1 − 0.9⁵ ≈ 0.41.
Common probabilities
| Event | Probability |
|---|---|
| Heads on a fair coin | 1/2 |
| A six on a fair die | 1/6 |
| A heart from a 52-card deck | 1/4 |
| Sum of 7 on two dice | 1/6 |
Conditional probability in daily life
The probability of rain given dark clouds is higher than the probability of rain overall. Reading P(A | B) carefully, and not confusing it with P(B | A), is the key to interpreting medical tests and many news claims.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- What is the chance of rolling two 4s with two fair dice?
Show answer
P(A and B), independent events: 0.027777778 · 2.77778% · 1/36
- P(A) = 0.6, P(B) = 0.5 and P(A and B) = 0.3. Find P(A or B).
Show answer
P(A or B): 0.8 · 80% · 4/5
Common mistakes to avoid
- Multiplying probabilities of events that are not independent.
- Adding P(A) and P(B) without subtracting the overlap.
- Entering percentages as whole numbers without the % sign. 25 is not a valid probability; use 25% or 0.25.
Frequently asked questions
What does independent mean?
Two events are independent if one happening does not change the chance of the other, like two separate coin flips.
What is conditional probability?
The probability of one event given that another has happened, written P(A | B).
What is the probability of at least one success?
Use the complement: 1 minus the probability of no successes.
Where can I practise?
Try the probability quiz.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.