# birthday.problem: Birthday problem In gennaro-tedesco/Rdice: A Collection of Functions to Experiment Dice Rolls

## Description

What is the probability that N different persons have the same birthdays?

## Usage

 `1` ```birthday.problem(days, people, gap, repetitions) ```

## Arguments

 `days` The total number N of possible choices per each occurrency; namely, for K occurrencies the total sample space is N^K. It defaults to the number of days in a regular year, i. e. 365. `people` The number of different cases whose coincidences we want to look at. In the example at hand the number of different people whose birthdays one wants to happen. `gap` The allowed gap between any two different cases. It defaults to 0, namely birthdays happening on the same day. `repetitions` The number of times one wants to repeat the experiment to derive the statistics. It defaults to 20000, that produces a relative error smaller than 0.5% in most relevant cases.

## Details

The function also provides the theoretical result, namely the theoretical probability that K cases can occurr simultaneously in the total sample space.

## Value

 `experiment` The frequency of success cases from the experiment, after the selected amount of repetitions. `theory` The theoretical probability value of K cases occurring simultaneously in the total sample space.

## Examples

 ```1 2 3 4``` ```## Simultaneous birthdays birthday.problem(people = 23) ## Birthdays one day apart birthday.problem(people = 23, gap = 1) ```

gennaro-tedesco/Rdice documentation built on May 17, 2019, 1:11 a.m.