Thread: Birthday probability

You are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?

http://en.wikipedia.org/wiki/Birthday_problem

suppose
x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 are present in room
x1= me
We can have sample space: { (x1,x2), (x1,x3)..(x1,x10) total 9
probability of all group have same DOB is 9/365
probability of all group does not have same DOB is 1-9/365

So money Earned by me is : 9/365 *$1
So money Earned by you is : 356/365 * $2