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How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50.......

+2 votes
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How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

posted Sep 1, 2020 by Maninder Bath

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1 Answer

+1 vote

Probabilty that 2 people in the group dont share a birthday
=(365/365)*(364/365)
Probabilty that 3 people in the group dont share a birthday
=(365/365)*(364/365)*(363/365)

Probabilty that n people dont share a birthday
(365!)/((365 - n)!*(365^n)) = P(no shared birthday)
By substitution we can see that for n = 23 the probability just drops below 0.5 and since the required probability is
1 - P(no shared birthday) = P(shared birthday)

answer Sep 2, 2020 by Tejas Naik



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