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Matching birthdays

Matching birthdays

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 5299.72
Birthdays 3652324.62
  1,0003840.30
  1,000,00011781253.98
UK National Lottery tickets 13,983,81644044687.47

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

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