Initially we have one red and one green ball in a box. At each
step we choose a ball randomly from the box,
look at its color and then return it
in the box with an additional ball of the same color. This way there will be 3 balls
in the box after the rst step, 4 balls after the 2nd step, and so on. Let X denote
the number of red balls in the box after the 1000th step. Find the probability mass
function of X.