Probability Calculator
Choose the type of problem and enter the probabilities. Type them as decimals, fractions such as 1/6, or percentages such as 25%. You get the combined chances and the working.
Worked examples
Independent events
Heads 1/2, six on a die 1/6
Both 1/12 (8.33%)
1/2 × 1/6.
Repeated trials
Chance 1/6, six times
At least one: 66.51%
1 - (5/6)^6.
About Probability Calculator
Probability measures how likely something is, from 0, which is impossible, to 1, which is certain. For independent events, where one does not affect the other, the chance of both is the two probabilities multiplied. The chance of at least one is the sum minus the chance of both, so that the overlap is not counted twice. A coin landing heads and a die showing a six has a chance of 1/2 × 1/6, which is 1/12.
If two events cannot both happen, such as a die showing a 2 and a 5 on the same roll, the chance of either is simply the sum. When you know the chance of both together, you can find a conditional probability: the chance of A given that B has happened is P(A and B) divided by P(B). The last option covers repeated trials: the chance of at least one success, none, or every time, and how many tries you need to reach a target chance. Answers appear as decimals, percentages and fractions.
How to use Probability Calculator
- Choose the type of problem from the list.
- Enter the chances as decimals, fractions such as 1/6, or percentages such as 25%.
- For conditional problems, add the chance of both events together. For repeated trials, add the number of times.
- Read the results and the explanation of each one.
Common uses
- GCSE and A level probability questions
- Chances in games, dice and cards
- Risk of at least one failure in repeated tries
- Working out conditional chances such as test accuracy
Frequently asked questions
How do I find the chance of at least one success?
Take 1 minus the chance of none. For a fair die rolled 6 times, the chance of no sixes is (5/6)^6, so the chance of at least one is about 66.5%.
What does independent mean?
Two events are independent when the result of one does not change the chance of the other, like two separate coin tosses.
What does mutually exclusive mean?
It means the events cannot both happen. Rolling a 2 and rolling a 5 on a single throw are mutually exclusive.
What is conditional probability?
It is the chance of one event given that another has happened. P(A given B) is P(A and B) divided by P(B).
How do I enter a probability?
As a decimal from 0 to 1, a fraction such as 1/6, or a percentage with a % sign. Percentages without the sign are not accepted, to avoid confusion.