Would you bet even money that there would be two kids in a class of 25 that had the same birthday?

[Charles]

So you have 25 random people. Is there a greater than 50% chance that two of them have the same birthday?

[Xavier Tremely]

My first thought is no.

[Charles]

My first thought is no.

Do you know any elementary school teachers? Ask them. I'd bet they'd all tell you yes. Not because they performed a statistical analysis of this problem but because they have lots of data. They see random groups of 25 or so kids year after year and they probably become aware of birthdays and I'm sure they would tell you more often then not there are two kids in the class with the same birthday.

[Chachma v'Oz]

I remember that the answer is "yes", but I don't remember the calculation that produces it. It's elementary probability theory.

[Chachma v'Oz]

If you want to start a big argument about probabilities, introduce the Monty Hall problem.

[Ratbag]

So you have 25 random people. Is there a greater than 50% chance that two of them have the same birthday?

25 kids in a class is not the same thing as 25 random people, are we talking a class where they are all the same year? in my childrens classes there are kids spread over 4 years of age, or are you only talking the day and not the month? these are huge differences

[Chachma v'Oz]

The question said "birthday", not "birth date".

[garyd]

That used to be one of the first problems they gave you in intro statistics and probability... The answer is yes. Bythe way by the time you get to a group of thirty it is statistically almost certainty.

[Charles]

That used to be one of the first problems they gave you in intro statistics and probability... The answer is yes. Bythe way by the time you get to a group of thirty it is statistically almost certainty.

Yep, I think at 22.4 kids it is 50/50 then it rise to the 57% when you hit 25 kids.

Imagine a matrix N kids by N kids. Take away the diagonal and take away one half of what is left. (The diagonal represents one kids asking himselft and bill compared to joe is the same as joe compared to bill that's why you take out one half of the matrix.

So what is left is (N^2 - N)/2 tests. (A test is seeing if the birthdays are the same.)

So, the probability of each test being Yes is 1/365, or NO is 364/365.

So what is the probability of all No? it is (364/365) ^ ((n^2 - )/2).

And the probability of all yes is 1 - the probability of all no.

So with N = 25, the probability of all NO is 43% which means at least one yes is 57%.

[garyd]

Another interesting probability question you have a six sided die it is not load or anything of the sort you have just rolled 5 sixes in a row. What are the chances that your sixth tos of the die will also come up a six?

[Chachma v'Oz]

One in six, unless it bears a six on more than one side.