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Complex Birthday Paradox Questions - Please read the 3 below.?
What is the formula for finding the chances of 3 people in a room or N people having the same birthday?
How about 2 people in a room of N people having the same birth Month - assuming 12 equal sized months?
How about requiring a percentage - like 90% - chance of at least 3 people having the same birthday in a room - how many people would we need?
I've looked for these formulae investigating permutations and combinations and the original birthday paradox which is 1 - (364/365)^[(n^2-n)/2]
1 Answer
- 1 decade agoFavorite Answer
The rule for the birthday problem is
365Pn / 365^n
where n is the number of people
The result is the probability that no one has the same birthday
If you find the compliment
1 − 365Pn / 365^n
the result is the probability that at least one pair of people will have the same birthday
The probability that three people will have the same birthday is
(1/365)^(3-1)