In a group of 23 people the chances are better than evens that two will share a birthday. Consider a variety of other random choices, such as thinking of a playing card, picking a lottery ticket, etc. Say that we have a match if there are two people that make the same choice.

Q: 1. How many people do we need for the probability of a match to be better than evens?

Q: 2. If we ask the birthdays (or whatever) of a *sequence*
of people, what's the expected number until we find the first match?

[TB, 24 Jan 2002]

A:

Probability | Question 1 | Question 2 | |
---|---|---|---|

1 in | # people | # people (2dp) | |

Cards in a pack | 52 | 9 | 9.72 |

Birthdays | 365 | 23 | 24.62 |

1,000 | 38 | 40.30 | |

1,000,000 | 1178 | 1253.98 | |

UK National Lottery tickets | 13,983,816 | 4404 | 4687.47 |

The last two involve Stirling approximations, but are probably correct as quoted.

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