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]
|Probability||Question 1||Question 2|
|1 in||# people||# people (2dp)|
|Cards in a pack||52||9||9.72|
|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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