Birthday Paradox Simulator
Birthday paradox calculator: the exact probability of a shared birthday in a group of n, with a repeated simulation that converges on the exact value.
At a glance
- Computes
- Exact probability that two people in a group share a birthday, plus simulated runs.
- You supply
- Group size, number of possible days, trials per run, and a seed.
- Use when
- You need the exact collision probability, or a demonstration that intuition fails.
- Assumes
- Birthdays uniform over the chosen number of days, and independent between people.
Exact probability
Ready
At least one shared birthday.
- Simulated probability
- Not run
- Pairs compared
- 253
- Trials completed
- Not run
The pair count grows as n(n - 1) / 2.
Run the simulation to fill Monte Carlo metrics and convergence.
Probability against Trial; reference at Exact probability
| Trial | Matching trials | Simulated probability |
|---|
Exact probability against People
P(match) = 1 - product((days - i) / days), i = 0..people - 1
How?
How this is calculated
The exact calculation multiplies the probability that each new person has a birthday not already seen, then takes the complement. The simulation assigns random day numbers and records whether any birthday repeats.
Formula: P(match) = 1 - product((days - i) / days), i = 0..people - 1
Sources
- Wolfram MathWorld Birthday Problem. Wolfram MathWorld. Retrieved .
Method last reviewed