8 and no match....... can anyone explane the math of this to me? |
to answer my own question :
http://en.wikipedia.org/wiki/Birthday_Paradox |
Philipp, you've slightly misstated the nature of the Birthday Puzzle:
"<I>(if 23 people are in a room, chances are above average there’s someone with your birthday)</I>"
Actually, if there are 23 people in a room, chances are above that two of them have the same birthday. The chances are only 1 in 13 that you are one of those two people. As you might expect, you'd need 365/2 people in a room for a 50% chance of having a birthday buddy of your own. |
Sorry, I meant '1 in 12' that you are one of those two people. |
Another probability puzzler many people get intuitively wrong is the Monty Hall problem:
http://en.wikipedia.org/wiki/Monty_Hall_problem |
Actually, Kevin Fox's comment is wrong. Having 183 people in a room still doesn't give you a 50% chance that spmeone in the room has the same birthday as you. Not everyone in the room is going to have different birthdays. Of those 183 people, most likely less than 183 days of the year will be represented, due to overlaps and shared birthdays between those 183 other people.
This easiest way to calculate the odds of someone sharing your specific birthday is to think of the opposite – that is, the chances of no one having the same birthday as you. For one other person in the room, that's (364/365) (i.e., there's only a 1/365 chance of having the same birthday). For two people in the room besides yourself, the chances of neither having the same birthday as your are (364/365)*(364/365). Generally speaking, for n other people in the room, the chances of none of the n sharing the same birthday as yourself are (364/365)^n.
Solving for n where (364/365)^n = .5 gives n = log .5 / log (364/365) = 252.65. So there need to be 253 other people in the room to have a >50% chance of someone there having the same birthday as yourself (i.e., a <50% chance that no one has the same birthday as you).
The "Birthday Paradox", of course, is different because it speaks to *any* two people in the room sharing a birthday. It just goes to show you that statistics aren't always intuitive... |
Bob's totally right. My bad. |
"The Birthday Paradox House
Thanks for coming to room 2!
Cool! You and Miek matched birthdays. There were 28 people inside the room at that time.
The probability of this happening was 68.096%.
Your names and birthday will be listed at the live data from all rooms.
This room will be emptied now. You can join it again and invite some friends to the party."
|
To be more accurate, at 23 or 24 people there's a slightly more than 50% chance that two will have the same birthday. |
