Probability Calculator
The probability and odds of an event, of two independent events together, or of successes over repeated tries.
Your chances
Filled in with example values. Replace them with your own.
Results update as you type.
Result
P = 1/6 = 0.166667 = 16.67%
Probability
16.67%
- As a decimal
- 0.166667
- Odds forFavourable : unfavourable
- 1 : 5
- Odds against
- 5 : 1
- Probability it does not happen
- 83.33%
How it’s calculated
Probability
1 ÷ 6 = 0.166667
How the probability calculator works
Choose a question. For one event, enter the favourable and possible outcomes. For two independent events, enter each chance to see the probability that both, either, exactly one or neither happen. For repeated tries, enter the chance each time and the number of tries.
Probabilities can be typed as a decimal (0.25), a percentage (25%) or a fraction (1/4).
The formulas
P(event) = favourable ÷ possible outcomes
P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) − P(A) × P(B)
P(at least once in n) = 1 − (1 − p)ⁿ
P(exactly k in n) = C(n, k) × pᵏ × (1 − p)ⁿ⁻ᵏ
Worked examples
- Rolling a 6: 1 ÷ 6 ≈ 16.67%, odds 1 : 5.
- Heads and a 6: ½ × 1/6 = 1/12 ≈ 8.33%; heads or a 6: 7/12 ≈ 58.33%.
- At least one 6 in 4 rolls: 1 − (5/6)⁴ ≈ 51.77%.
- Exactly two 6s in 10 rolls: C(10, 2) × (1/6)² × (5/6)⁸ ≈ 29.07%.
Assumptions
- Outcomes in the first mode are equally likely.
- Events and tries are independent, with the same chance each time.
Frequently asked questions
What is the difference between probability and odds?
Probability compares favourable outcomes with all outcomes: rolling a 6 is 1 in 6. Odds compare favourable with unfavourable outcomes: 1 to 5 for, or 5 to 1 against.
What does independent mean?
Two events are independent when one happening does not change the chance of the other, like two separate dice rolls. The two-event formulas here only apply to independent events.
If something has a 1 in 6 chance, will it happen in 6 tries?
Not necessarily. The chance of at least one 6 in 6 rolls is 1 − (5/6)⁶ ≈ 66.5%, not 100%. Each roll is a fresh chance.
What is “exactly k” based on?
The binomial distribution: the number of ways to choose which k tries succeed, C(n, k), times the chance of k successes and n − k failures.