OT - Birthdays
- From: "wingnut" <cpark429@xxxxxxxxxxxxxx>
- Date: Sun, 22 Jan 2006 04:10:05 GMT
If you have 25 people, there are exactly 300 possible
different pairings (24x25/2).
for any individual pair, the probability that their
birthdays are DIFFERENT is 364/365. For 2 diffierent pairs
the probability that BOTH pairs have different birthdays is
364/365 times 364/365. This relationship holds for any
number of pairs of people, that is for n different pairs,
the probability that all have different birthdays is the
product of 364/365 with itself n times.
Now it turns out that if you multiply 364/365 times itself
300 times you get a number that is slightly less than 1/2
(approximately .4391). This number is the probability that
all 300 pairs have different birthdays. So subtracting that
number from 1 gives a number which is slightly more than 1/2
(.5609) which is the probability that AT LEAST ONE of the
pairs has the same birthday.
As it turns out, if you have only 24 people, the total
number of pairs drops to 276. 364/365 raised to the 276
power is approximately .4690 which is less than 1/2, so the
probability that at least two will have the same birthday is
still greater than 1/2 (.531) . However for 23 people or
less, the probablilty is less than 1/2.
if you have 30 people, the probability that at least 2
people have the same birthday rises to almost .70
Mathematicians do it by the numbers.
Wingnut
.
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