if I remember correct, if you want the probability of two people in a group having the same birthdate to rise above 50%, you need like 20-25 people in the group.
right?
so I was wondering how many people your group would need in order for the probability of two people having the same birth_time_ (and still date) rise above 50%?
any math pros? thanks
For this question to be answerable, you need to be more precise about what you mean by “birth time”. Do you mean that the clock read the same time, down to, say, the second, during each birth? Or do you only require that the clock read the same down to the minute? Or down to the millisecond?
Obviously, the narrower that you make the time-window, the lower the probability, because you increase the number of such time-windows in a year.
I believe the probability of two people being born at the precise same instant is zero since that instant is a mathematical point (zero length) in time. As Tyrrell McAllister said, you have specify some interval of time. The longer the interval the higher the probability and vice versa.
Taking “birth time” to mean the day, hour and minute of birth, you can calculate the probability that n people all have different birth times as follows:
525,959 x 525,958 x 525,957 x … x (525,960 - n + 1) divided by 525,960[sup]n - 1[/sup]. The probability that at least two people share a birth time is then one minus that result. The figure 525,960 is just the number of minutes in a year (365.25 x 24 x 60).
By my calculations, you’d need 855 people.
This serves as a good illustration of what’s going on in such problems and why the numbers needed may be surprisingly small. As the number of people grows, the number of pairs of people, and hence candidates for matches, inreases roughly as the square of the number of people. A match to the minute is 1440 times less likely than a match to the day (assuming, as we are, that birth times are uniformly distributed). It only takes about the square root of 1440 times more people to have a 50% chance of a match; if you take 23 (the answer for matches to the day) and multiply by sqrt(1440), you get about 873, not too far from 855.