# Talk:Birthday problem

## usage of people

Why assume that the people choosen are alive?   If dead, then "they" aren't people, but corpses.   The task clearly states a group of people.   However, even if dead, they still had a birthday. -- Gerard Schildberger (talk) 03:02, 4 November 2013 (UTC)

## years in Algol

What does years signify in "%age of years with required common birthdays: 50.71%;" ? --Walterpachl (talk) 10:36, 4 November 2013 (UTC)

## Meaning of precision

I’m not sure what “Estimating the error in the estimate to help ensure the estimate is accurate to 4 decimal places” means. My interpretation is that the ${\displaystyle \sigma _{\mathrm {mean} }}$ of the estimated frequency is ${\displaystyle <1/10000}$.

The ${\displaystyle \sigma _{\mathrm {mean} }}$ of the distribution of each sample is calculated using the binomial distribution, so it’s is at most ${\displaystyle 1/2}$ (for ${\displaystyle p=q=1/2}$). We are very near that value. In this case, if we use ${\displaystyle \sigma _{\mathrm {mean} }=\sigma /Sqrt(N)}$ then the number of samples has to be ${\displaystyle N=25000000=10000^{2}/4}$.

Most of the examples use ${\displaystyle N=50000}$, so they don’t have enough precision. On the other hand, ${\displaystyle 25000000}$ is to much, so I run my example in Racket with only ${\displaystyle 250000}$, that gives a ${\displaystyle \sigma }$ of only ${\displaystyle 1/1000}$.

I think that the description of the task should ask for a clearer goal. For example: “Do the final simulation with at least 25000000 samples to help ensure the estimate is accurate to 3 decimal places.”