Subject: Incidence of birthdays
Date: Sat 11/7/98 3:00 AM
From: Bob Thomas
I've been familiar with the birthday paradox since i was a child and my father, at parties, would have fun betting someone that the first 35 people he picked would have at least one birthday match.
My question involves the underlying theory: why does the problem have to be solved backward, i.e. figuring the odds of there being no match and subtracting that value from 1.
Now i see that the arithmetic doesn't support a straightforward approach, that, for example, 1/365 x 2/365 does not equal 1 - (364/365 x 363/365) but i don't see the logic of why it doesn't. Put it another way, if the second person has a 1/365 chance of matching the first's birthday and the third person has a 2/365 chance of matching one of the first two why can't we multiply those to get the chance that 3 people will share a birtday the same way we multiply the chance that the second WON'T match the first (364/365) by the chance that the third WON'T match either (363/365) ?
Hope there is a simple why-didn't-i-think-of-that answer, but having not found it even addressed on several sites on the birthday problem i suspect that may not be the case.
In any event, thank you for your consideration and even more if you send back the explanation. -- bob thomas