Probability
Probability Calculator
Probability of A and B, A or B, not A, and exactly one — for two independent events given their individual probabilities.
P(A∩B) = P(A)·P(B)
Also called probability of events · p(a and b)
Math · 11 calculators
Probability Calculators
Probability of events, combinations and permutations, binomial distributions, odds, dice and coin flips.
Probability
Conditional Probability Calculator
Compute P(A|B) from P(A and B) and P(B), or use Bayes’ theorem with P(B|A), P(A) and P(B).
P(A|B) = P(A∩B)/P(B) = P(B|A)·P(A)/P(B)
Also called bayes theorem calculator · p(a given b)
Probability
Independent Events Calculator
Probability that an event happens at least once, every time or never over repeated independent trials.
P(at least one) = 1 − (1 − p)ⁿ
Also called at least once probability · repeated trials
Probability
Combination Calculator
Number of ways to choose r items from n when order does not matter (nCr), with and without repetition.
C(n, r) = n! / (r!(n − r)!)
Also called ncr calculator · n choose r
Probability
Permutation Calculator
Count arrangements of r items from n when order matters (nPr), with and without repetition.
P(n, r) = n! / (n − r)!
Also called npr calculator · arrangements calculator
Probability
Binomial Probability Calculator
Probability of exactly, at most or at least k successes in n independent trials, with mean and standard deviation.
P(X = k) = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ
Also called binomial distribution calculator · binomial pmf
Probability
Expected Value Calculator
Expected value, variance and standard deviation of a discrete random variable from outcomes and probabilities.
E[X] = Σ xᵢ·pᵢ
Also called ev calculator · mean of random variable
Probability
Odds Calculator
Convert between odds (for/against), probability and fractional/decimal betting odds, with implied probability.
P = a / (a + b)
Also called odds to probability · probability to odds
Probability
Dice Probability Calculator
Probability of rolling an exact sum, at least or at most a total with any number of dice and sides (d6, d20…).
P = favourable outcomes / sidesⁿ
Also called dice roll probability · dice odds
Probability
Coin Flip Probability Calculator
Probability of getting exactly, at least or at most k heads in n coin tosses, for fair or biased coins.
P = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ
Also called coin toss probability · heads or tails probability
Probability
Birthday Probability Calculator
The birthday paradox: chance that at least two people in a group share a birthday — 23 people already gives over 50%.
P = 1 − (365/365)(364/365)…((365 − n + 1)…
Also called birthday paradox · shared birthday probability
Key probability formulas
| Probability | P(A∩B) = P(A)·P(B) · P(A∪B) = P(A) + P(B) − P(A∩B) |
|---|---|
| Conditional Probability | P(A|B) = P(A∩B)/P(B) = P(B|A)·P(A)/P(B) |
| Independent Events | P(at least one) = 1 − (1 − p)ⁿ |
| Combination | C(n, r) = n! / (r!(n − r)!) |
| Permutation | P(n, r) = n! / (n − r)! |
| Binomial Probability | P(X = k) = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ |
| Expected Value | E[X] = Σ xᵢ·pᵢ |
| Odds | P = a / (a + b) · decimal odds = 1 / P |
| Dice Probability | P = favourable outcomes / sidesⁿ |
| Coin Flip Probability | P = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ |