Quote:
Originally posted by wiZd0m:
oh, and it's not near 80% the chance of getting 2 people on the same bday it's more less than 1/12
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There's a 1 in 12 chance? You're WAY off! You've just proved yourself wrong. See how common sense tells you one thing, when the truth is the other. This always happens with stats. People think the gambling machine that hasn't paid out in a while has more chance of a pay out - it doesn't matter!
Let me do the math for you: I'll figure out the chance that NO ONE has the same birthday, thus proving it backwards.
person 1 has a birthday.
person 2 has a birthday - 364/365 chance of not having the same birthday. chances are 99.7% that no one has the same b-day
person 3 has a 363/365 chance of not having the same birthday as the first two. take the 99.7% chance, and multiply this with the 99.4% chance that the 3rd guy has a b-day with the other two. this makes 364/365 * 363/365 = 99.1% chance
let's do this 30 times:
364/365 * 363/365 * 362/365 * .... 335/365 =
364! / 334! / 365^30 = 26.95% chance that everyone in the class has a different birthday.
100 - 26.95 =
73.0454633% chance that in a 30-person class, two of the perons (assuming no twins) have the same birthday 
who would have guessed?
the answer would be slightly modified if i took feb 29 into account, but not by much.
Where did you go wrong? I'll tell you the most common error:
the chances of a person in the class of 30 having the same b-day as another IS NOT THE SAME CHANCE as you having the same birthday as someone in a 30-person class. The chances of that are 8.2%.
cheers everyone,
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