Probability Calculator
The probability of a single event is favourable outcomes divided by total equally likely outcomes: P(A) = favourable ÷ total, always between 0 (impossible) and 1 (certain).
Enter Values
How to use this calculator
- Enter the number of favourable outcomes and the total number of equally likely outcomes for Event A (e.g. 1 and 6 for rolling a specific number on a die).
- To combine two independent events, also fill in the favourable and total outcomes for Event B — you'll get P(A and B), P(A or B) and P(neither).
- Read each result as both a decimal probability (0 to 1) and a percentage; multiply by 100 to convert, or leave B blank if you only need a single event.
How it works
The probability of a single event is favourable outcomes divided by total equally likely outcomes: P(A) = favourable ÷ total, always between 0 (impossible) and 1 (certain). The complement, the chance it does NOT happen, is P(not A) = 1 − P(A).
For two independent events the calculator applies the standard rules: multiplication P(A and B) = P(A) × P(B), addition P(A or B) = P(A) + P(B) − P(A) × P(B), and P(neither) = (1 − P(A)) × (1 − P(B)). These assume the events don't influence each other; dependent events need conditional probability.
Worked example
Rolling a 6 and flipping heads. Event A is rolling a 6 on a fair die: 1 favourable outcome out of 6, so P(A) = 1 ÷ 6 = 0.166667 (16.6667%). Event B is a coin landing heads: 1 out of 2, so P(B) = 0.5. Because the roll and the flip are independent, P(A and B) = 0.166667 × 0.5 = 0.083333 (8.3333%), and P(A or B) = 0.166667 + 0.5 − 0.083333 = 0.583333 (58.3333%). The chance of neither happening is (1 − 0.166667) × (1 − 0.5) = 0.416667.
Common mistakes
- Adding P(A) and P(B) directly for 'A or B'. That double-counts the overlap — you must subtract P(A and B), giving P(A) + P(B) − P(A)×P(B).
- Using the multiplication rule for events that are not independent. P(A and B) = P(A) × P(B) only holds when one event has no effect on the other; drawing cards without replacement, for example, is dependent.
- Entering more favourable outcomes than total outcomes, which would give a probability above 1 — a probability can never exceed 1 (100%).
Frequently asked questions
How do I calculate the probability of two things both happening?
For two independent events, multiply their individual probabilities: P(A and B) = P(A) × P(B). For example, a 1/6 chance and a 1/2 chance combine to 1/6 × 1/2 = 1/12 ≈ 0.0833 (8.33%). This only works when the events don't affect each other.
What is the probability of A or B happening?
Use the addition rule: P(A or B) = P(A) + P(B) − P(A and B). You subtract the overlap so it isn't counted twice. For independent events that becomes P(A) + P(B) − P(A) × P(B).
Can a probability be greater than 1?
No. A probability is always between 0 and 1 (0% to 100%). If your favourable outcomes exceed the total number of outcomes you've made an input error — the calculator will flag it.
Does this calculator assume the events are independent?
Yes. The two-event results (A and B, A or B, neither) assume Event A and Event B are independent — the outcome of one doesn't change the other. For dependent events, such as drawing cards without replacement, you'd use conditional probability instead.
Related tools
- Normal Distribution Calculator
- Permutations Calculator
- Combinations Calculator
- Binomial Probability Calculator
- Conditional Probability Calculator
- Confidence Interval Calculator
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Tip: Enter any known values to calculate the remaining results.
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