Probability Calculator

Combinatorics and probability distribution calculations.

n (total items)

r (selected items)

nPr (permutations)

nCr (combinations)

nPr = n! / (n-r)! | nCr = n! / (r! × (n-r)!)

n (trials)

k (successes)

p (probability)

P(X = k) - PMF

P(X ≤ k) - CDF

μ (mean)

σ (std dev)

x (value)

Z-score

P(X ≤ x) - CDF

Common Z-scores: 1.645 (90%), 1.96 (95%), 2.576 (99%)

Number of people

Probability of shared birthday

With 23 people, there is a ~50% chance that two share a birthday.

With 70 people, it is ~99.9% likely.

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