Question 238028: A statistics class contains 10 students. What is the probability that no two students have the same birthday?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Out of 10 people you have 45 possible pairings of different people in each pair.
This would be a combination and the formula would be n! / (x!*(n-1)!)
With each one of these pairings, the probability that the two persons involved do NOT have the same birthday would be 364 / 365 if we ignore february 29th.
The probability that all of these pairing would NOT have the same birthday is therefore (364/365)^45 = .883859763
This means that there's at least a 12% chance that one of them will have the same birthday.
If I include February 29th, then the total possible birthdays becomes 366.
The probability of not being both on the same day is then 365/366 which changes the results a little but not much.
Numbers become (365/366)^45 = .88415836
we're still talking about 12% chance of at least one of the pairs being born on the same day.
I don't know if I calculated the february 29th probability correctly, but even if not, the difference would still be negligible.
That's what I think.
I checked the logic with smaller numbers and it appears to be sound.
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