Originally posted by Moskeeto
When I took statistics, my teacher tried to explain it to us, but she got too confused and quit. Its something about breaking it down into 1/12 chance of being the same month then a 1/30 chance of being the same day. it doesn't make much sense to me, but i'm not very smart.
Here's a semi-mathematical explanation which I just thought of, and may be wrong
:
Basically, let's say that there are 30 people (numbered from 1 to 30). The probability of person 1 having the same birthday as any of the 29 other people is 29/365, or almost 8%.
But you have to consider the probability of person #2 having the same birthday as any of the other 29. You already considered #1 and #2 having the same birthday, so instead of having an additional 8% (29/365) to add to the original 8% (29/365), you have to add 28/365 (or 7.6%).
For person #3, you have possible birthday matches with #4, 5, 6, etc all the way to 30, or 27 possible matches. This is another 7.4%.
So after only 3 people, you already have a semi-decent chance of 2 people having the same birthday. Unfortunately, you can't just add the probabilities here, since it doesn't work that way (for example, if you roll a 6 sided die, the odds of getting a 1 are 1/6th. However, if you roll it 6 times, the odds of getting a 1 at least once is not 6 times 1/6 (or 100%). It's less than that.)
So anyway, theoretically, all those birthday probabilities add up to somewhere around 50%.
Hope that didn't confuse anyone even more...
ttac