Mathematical Puzzle

[libya 115]

I read a book review in the 'Bangkok Post' on Thursday or Friday last week, about probability, and this is what I do not understand:

It states that in order that two people share the same birthday only 23 in a room will yield a better than 50% chance.

Can anyone explain that? I know it is not a misprint because I have read that very same fact before somewhere.

There must be some probability mathematicians out there.........?????

[Ijustwannateach]

I don't have pencil, paper, or calculator with me, but I think I can help make it less mysterious.

The thing that makes it seem impossible is when you assume that two PARTICULAR people must have the same PARTICULAR birthday. It becomes much more likely that ANY two people will share ANY birthday.

Let's say you come up with the probablity for 2 people out of this group to share the birthday of January 1st. Whatever number you come up with for this day would hold equally for every other day in the year- so you would have to accumulate all those probabilities to arrive at a final probability for any two in a group of 23 to have the same birthday.

I'll look at this again in a day or so and if no one's tried to do the math I will- I gotta run now.

"Steven"

[solo siam]

http://www.maa.org/mathland/mathtrek_11_23_98.html

[Thetyim]

http://www.people.virginia.edu/~rjh9u/birthday.html

[suegha]

These links were a big help, isn't math fantastic!

[Sir Burr]

isn't math fantastic!

Maths, the language of God.

[libya 115]

Thanks for the replies; I still feel a bit puzzled that only 23 people need to be in the room for a 50% chance. Would that mean (for example) 46 for a 99.99% chance?

Sure, that must be wrong.

So where is the 'missing gap' I am puzzled further...!!??