# Math Help - Red and Black balls in urn

1. ## Red and Black balls in urn

An urn contains n+m balls, n red and m black
let X be the number of red balls chosen without replacement before a black one is chosen. We are intressted in E(x). To obtain this quantity, number red balls from 1 to n and define Xi, i=1,...,n by
Xi{ 1 of red ball i is chosen ,
0 otherwise

so i get what's going on....firstly, the probability of drawing a red ball is n/n+m...and i need to show that the answer is the mean of a geometric dist: 1/p.

So i need to write E(x)= summation of i from 1 to n (xi)
but i don't know how to proceed... something like sum(xi* P(xi))... i dont really know how to insert the notation either

2. I got the following recursive expression for your problem

E(x) which I prefer to write as E(n,m) as it is a function of n,m

E(n,m) = n/(n+m) E(n-1,m) + 1

Note the end condition E(0,m) = 1