Question

In a group of 15 people, what is the probability that two or more of them have the same birthday? (answer is 0.2529)

Answer 1

This is also best solved using complements, i.e. what is the probability that no two people share a birthday?

Answer 2

I used the formula 1- ((365*364......(365-r+1) ) / (365)^r

Answer 3

That might work . . . I'm trying to simplify the formula I usually use to see if it's the same.

Answer 4

But I got the wrong answer..I ended up getting something close to 0.9

Answer 5

Ok, try making this adjustment to your formula:
1- ((364*363......(365-r+1) ) / (365)^(r-1)

Answer 6

What is the formula that you usually use?

Answer 7

I usually never bother with formulas, I just imagine the situation and build up my own expression.
For this scenario, I think of it as trying to determine the probability of no two people out of 15 sharing a birthday.
First person shares a birthday with himself, so I ignore that, P(second person not sharing birthday with first person) = 364/365; P(third person not sharing a birthday with first or second person) = 363/365), and so on. I then multiply all those probabilities together to find P(no two share a birthday).

i subtract that from 1 to find P(of at least two share..)