Birthday collisions
How small can a group be before matching birthdays become likely? Predict, generate groups and inspect the matches.
Find the surprising threshold
1 question · No time limit
Example
Example
Is the probability of a shared birthday above or below 25%?
Group A: 17 people, 365 possible dates. At least two people must share any date. Every date is equally likely, and people’s dates are independent. Dates are numbered from 1 to 365; ignore leap days.
1. Predict
Group A
People: 17 · Possible dates: 365
At least two people share any date
Generate a group to inspect its dates.
Make a prediction first. It is not scored.
2. Test your idea
- Groups generated
- 0
- Group A: Observed frequency
- …
- Comparison threshold
- 25%
These are random trials, not exact probabilities.
Try the controls, then check your solution.
Why?
For Group A, all dates differ with probability 365/365 × 364/365 × … × 349/365. Subtract from 1 to get the chance of at least one shared date: 31.5%.
The exact probability is above 25%. The displayed percentages are rounded; the comparison uses exact whole-number counts.
Revisit your prediction
Keep exploring the experiment.
3. Change the rules
A linked challenge. This answer is not scored.
Continue your unfinished round
Your answers are saved in this tab. Continue from where you left off.
Continuing uses no additional practice start.
Discard the unfinished round?
Your answers from this round will be discarded. You can choose your settings before starting a new round.
Starting the new round uses one practice start.
- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Try the controls, then check your solution.
Your first checked solution is recorded. You can keep experimenting afterwards.
About this practice
Learn a method
Count birthday collisionsHow small can a group be before matching birthdays become likely? Predict, generate groups and inspect the matches.
For a broader mix of practices, explore the probability practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used