The birthday problem is a statistical phenomenon where the chances two people in a room have the same birthday are far higher than intuitively expected. For example, the likelihood that two people in a room of 23 share a birthday is around 50%. Most people would expect (given an even distribution of births) you would need 365 / 2 = 183 people to have a 50-50 chance that two have the same birthday. The actual results are below:
| n | Probability |
|---|---|
| 1 | 0% |
| 10 | 11.7% |
| 23 | 50.7% |
| 30 | 70.6% |
| 50 | 97% |
| 70 | 99.9% |
| 100 | 99.999% |
I built a Rust program to experimentally validate this. You can run as:
cargo run <n>
If no number is specified, n will default to 23.