There was one probability question, in which i solved last night, and it was like real tough ( for me),and as im not able to check whether my working and answer is correct, i shall post my workings here and hopefully you guys can tell me where i am wrong exactly etc...

this is the question:

consider an urn that contains r red and g green balls. A ball is drawn at random and it6s color is noted. Then the ball with balls of the same colur, are returned to the urn. Suppose "n" such draws are made from the urn, show that the probability of selecting a read ball at any draw is (its just greater than not greater than and equal to zero.)

I start by going, = event that the mth ball drawn is red. =event that i red balls are observed up to the (m-1)th draw.

So probability of drawing i red balls in the first i successive draw is:   up to this stage its pretty fine, but from here i dont even know what i was doing..

anyway coming back to   where i just made a substitution of :   FInally its now like this:       then so so actually the summation: which gives:: Yea this is my approach, though during my computation in the binomial part i might have made some mistakes, but i still arrived at what the question wanted. I will appreciate if anyone could correct if i made any mistakes,.

THank you