At The Next Big Party You Attend, (25 or More People) Wanna Give Everyone A Laugh And Win Bets?

Let's say you're with friends at a sizable party, 25 or more people. You say, (to the "smart Alec" of your group), "I'll bet you or anyone, that there are at least two people here with the same birthdate - exclusive of twins or triplets." You look around - the other conversations are stopping. You add, "And I have no pre-knowledge of anyone's birthday." You can almost see everyone's mental gears meshing: 365 days in the year, only 25 or so people here! Someone asks, "What's the gimmick?

And you are serious. What the non-mathematicians do not figure is how the numbers in the problem accrue. Starting with two people at random - there is one possibility of a match, if their birth-dates are the same, versus 363 possibilities of a non-match. However, when another person is added, the probability of a match increases by 2 (in addition to the possibility of person "a" matching person "b", there is now the added possibilities of "a" matching "c" and of "b" matching "c"); the total possibilities are thus the sum of 1 + 2 = 3. Adding a fourth person makes the total number of possibilities: 1 +2 +3 = 6; and so on.

Thus for a random group of twenty people, the number of possible matches is 190 out of a year's 365 (or 366) days. far better than an even bet. If the group numbers 24, the probability of a match is 276, or better than three to one. When there are 30 or more people in the group, you can bet the farm. Have fun!

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