A jar contains n − 1 vanilla cookies and one chocolate cookie. You reach into the jar and choose a cookie at random. What is the probability that you will first get the chocolate cookie on the kth try...

A jar contains n − 1 vanilla cookies and one chocolate cookie. You reach into the jar and choose a cookie at random. What is the probability that you will first get the chocolate cookie on the kth try if you (a) eat (b) replace each cookie you select. Show that if n is large compared to k then the ratio of the probabilities in (a) and (b) is approximately 1.