Asked by Matt
A math class has 20 students who choose a topic from a list for an essay. How big pool is necessary for the probability of at least one duplicate to drop below fifty percent?
Answers
Answered by
drwls
This is a variation of the "birthday problem": the probability that in a group of n people, at least two will have the same birthday. (That number is 23 with 365 possible birthdays). In your case the number of people is 20 and you want to know the number of essay topics (analogous to the number of possible birthdays)
For the method, see http://www.npr.org/templates/story/story.php?storyId=4542341
The answer will probably be several hundred, but that is as far as I am going to go with it.
For the method, see http://www.npr.org/templates/story/story.php?storyId=4542341
The answer will probably be several hundred, but that is as far as I am going to go with it.
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