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How to use
This probability calculator keeps four common problem types separate: a single event from equally likely outcomes, two independent events, combinations and permutations, and binomial probability for a number of successes. Choosing the correct model matters more than simply entering numbers.
- Choose the problem type from the mode selector.
- Enter only the fields for that mode; probabilities accept forms such as 0.25, 25%, or 1/4.
- Calculate and read the outputs together with the independence warning for the two-event mode.
How it is calculated
Example
Example: rolling a 6 on a fair die gives 1/6 ≈ 16.67%, with a complement of about 83.33%. For counting, choosing 3 items from 10 without order gives C(10,3)=120, while arranging 3 from 10 gives P(10,3)=720.
Important notes
The simple-event ratio assumes elementary outcomes are equally likely. In this tool, P(A and B)=P(A)P(B) and the corresponding OR rule apply only to independent events. The binomial model assumes a fixed number of independent trials, constant success probability and two outcomes per trial. Use another model when those assumptions do not hold.
Worked examples and interpreting results
If six outcomes are equally likely and two satisfy an event, its probability is one third. For independent events with probabilities 0.5 and 0.25, the probability that both occur is 0.125.
| Case | Calculation | Result |
|---|---|---|
| Event from equally likely outcomes | 2 ÷ 6 | 0.333333 |
| Both independent events occur | 0.5 × 0.25 | 0.125 |
How to check the result
Do not multiply the probabilities this way without independence. Treating outcomes as equally likely is an assumption to verify. The outcome count must be positive and each probability between zero and one.
Frequently asked questions
When should I use combinations instead of permutations?
Use combinations when order does not matter and permutations when changing order creates a different outcome.
Is P(A or B) always just the sum?
No. The intersection must be subtracted to avoid double counting; this calculator obtains that intersection by multiplication only under independence.
What are the binomial assumptions?
A fixed number of trials, independent trials, a constant success probability and two outcome classes per trial.