A probability calculator finds the chance of an event by dividing favourable outcomes by total outcomes. Formula: P = favorable / total; headline shows P as a percent; detail also lists the decimal probability. Drawing a red marble when 3 of 10 are red has a probability of 0.3, or 30%.
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How to use the probability calculator
- Enter the number of favourable outcomes.
- Enter the total number of outcomes.
- Read the probability and percentage.
How the probability calculator works
The probability calculator uses the classical definition of probability. When every outcome is equally likely, the probability of an event is:
- P(event) = favourable outcomes ÷ total outcomes
You enter the number of favourable outcomes and the total number of possible outcomes. The tool shows the probability as a decimal to six places and as a percentage. The total must be more than zero, and favourable outcomes must be between zero and the total, so the answer always lies between 0 and 1.
Probability calculator worked example
A bag holds 10 marbles, 3 of them red. The chance of drawing a red marble is 3 ÷ 10 = 0.3, or 30%. A fair die has 6 faces, so rolling a four has probability 1 ÷ 6 ≈ 0.166667. A deck has 13 hearts among 52 cards, so P(heart) = 0.25. The probability calculator returns each of these in the table.
| Favourable | Total | Probability | Percent |
|---|---|---|---|
| 3 | 10 | 0.3 | 30.00% |
| 1 | 6 | 0.166667 | 16.67% |
| 13 | 52 | 0.25 | 25.00% |
| 4 | 52 | 0.076923 | 7.69% |
| 1 | 2 | 0.5 | 50.00% |
Complements and odds
The chance an event does not happen is 1 − P. If P(red) is 0.3, then P(not red) is 0.7. Odds are a different way to say the same thing: odds in favour are favourable to unfavourable, so 3 red and 7 other marbles give odds of 3 to 7, not 3 to 10. To turn odds of a to b into a probability, divide a by a + b.
Combining events
The tool handles one event at a time. For two independent events, multiply: the chance of two heads in two coin tosses is 0.5 × 0.5 = 0.25. For events that cannot both happen, add: rolling a 1 or a 2 is 1/6 + 1/6 = 1/3. If events overlap, subtract the overlap: P(heart or king) = 13/52 + 4/52 − 1/52 = 16/52. You can use the probability calculator for each part and then combine the results by hand.
Counting large totals
For cards, lotteries and committees the total can be large. Use combinations to count it. There are 2,598,960 five-card poker hands, and 4 of them are royal flushes, so P(royal flush) = 4 ÷ 2,598,960 ≈ 0.0000015. Enter those counts and the probability calculator gives the same result as a percentage.
When equally likely does not hold
The favourable ÷ total rule needs outcomes that are equally likely. A loaded die, the weather or a sports match do not meet that test. For those, probability comes from data: experimental probability is how often the event happened divided by the number of trials. If 18 of 60 days in a sample were rainy, the estimate is 0.3. Larger samples give steadier estimates, a result called the law of large numbers.
Common mistakes
The most common mistake is using unfavourable outcomes in place of the total. Another is counting outcomes that are not equally likely, such as treating the sums of two dice as 11 equal results when a sum of 7 is six times as likely as a sum of 2. A third is forgetting that drawing without replacement changes the total for the second draw: after one red marble is removed, the chance of a second red is 2 ÷ 9, not 3 ÷ 10. Think about each draw in turn when the bag or deck changes.
Tips
- Count favourable outcomes carefully and avoid double counting.
- Check that the total includes every possible outcome.
- Remember that 0 means impossible and 1 means certain.
- Use the probability calculator to check textbook answers.
Related converters and calculators
Related calculators:
- Permutation and combination calculator: count outcomes
- Dice roller: roll dice
- Statistics calculator: summary statistics
- Percentage calculator: percent
Sources
OpenStax Introductory Statistics 2e, 3.1: Terminology.
Formula and method
P = favorable / total; headline shows P as a percent; detail also lists the decimal probability.
Simple classical probability for equally likely outcomes. Requires total > 0 and 0 <= favorable <= total.
Questions about this calculator
What is the probability formula?
P = favourable ÷ total outcomes, for equally likely outcomes.
What is the chance of rolling a 6?
1/6, about 16.67%.
How do I find the chance of not happening?
1 − P.
Can I combine two events?
Not directly; multiply independent probabilities by hand.
What range can a probability take?
0 to 1.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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