Birthday chances
Thirteen friends at a dinner party talk about birthdays. They realize that two of them have their birthday on the same date. "How strange..." someone says. "There are 365 possible days and we are only 13. This must be a rare coincidence."
Is that true? Approximately what is the probability of two birthdays falling on the same date?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let us calculate the probability of NOT having two birthdays on the same date. With two people the probability is 364/365, because the first person "reserved" a date, and the second one can select between the 364 remaining days. When the third person is added, the probability will be (364/365)(363/365) since the 3rd person has only 363 choices. Generalizing:
p=(364/365)(363/365) ... (353/365) = 0.806
Therefore 1-p~20%. Not a rare coincidence at all!