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I dealt with one issue, namely: Consider $k$ independent realizations of a random variable uniformly distributed over a set of $n$ values.
1 What must $k$ be for the probability that the given outcome will be at least $\frac{1}{2}$?
2. What should $k$ be for the probability that a pair of equal outcomes will be at least $\frac{1}{2}$?

But then I was asked following questions:
At what minimum group size (group size means the size of the group of people) is the probability that there is a classmate born on the same day as you greater than $\frac{1}{2}$? At what minimum group size is the probability that there is a pair of classmates born on the same day greater than $\frac{1}{2}$?

I'm a little confused with this question. Could anyone help me? Thank you!

J. W. Tanner
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wxist
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  • What is confusing about the question specifically? Are you having trouble seeing how the two questions are different? Are you just having difficulty finding an approach? For both, consider the opposite scenario... that everyone's birthday is different than yours or that everyone's birthday is different than each other respectively. – JMoravitz Mar 17 '23 at 14:48
  • The words to search on are "birthday paradox" – Greg Martin Mar 17 '23 at 15:32
  • @JMoravitz I have troubles with approach to those questions – wxist Mar 17 '23 at 15:42

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