Probability Calculator
P(A) = favorable outcomes / total outcomes
C(n,r) = n! / (r! × (n−r)!) — order does not matter
P(n,r) = n! / (n−r)! — order matters
Result
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Formulas
Examples
Basic: Rolling a 4 or higher on a d6
Favorable: 3 (faces 4, 5, 6) — Total: 6 — P = 3/6 = 0.5 (50%)
Combinations: Choosing 3 from 10 people for a committee
C(10,3) = 10! / (3! × 7!) = 120 ways
Permutations: Awarding 1st/2nd/3rd from 10 runners
P(10,3) = 10! / 7! = 10 × 9 × 8 = 720 ways
When to Use Each
Frequently Asked Questions
What is probability?
Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1 (or 0% to 100%). P = 0 means impossible; P = 1 means certain. Rolling a 3 on a fair die has probability 1/6 ≈ 0.167 or 16.7%.
What is the difference between combinations and permutations?
Combinations count the number of ways to choose r items from n when order does not matter (e.g., selecting a lottery ticket). Permutations count ordered arrangements — where the sequence matters (e.g., awarding 1st, 2nd, 3rd place). For the same n and r, permutations ≥ combinations.
What is the complement rule?
The complement of event A is everything that is not A. P(not A) = 1 − P(A). If there is a 30% chance of rain, there is a 70% chance of no rain. The complement rule is useful for calculating the probability of "at least one" event.
Can probability be greater than 1?
No. Probability is always between 0 and 1 inclusive. If your calculation gives a result outside this range, check that you are dividing favorable outcomes by total outcomes, and that total outcomes includes all possible outcomes.