Problem 2. (12 pt) Ed is a contestant on a game show. He is presented with a bucket of n balls. The balls can be opened up; inside each ball is a check for some amount of money. Ed has no knowledge of the amounts written on the checks, but he is told that all the n amounts are different. Here are the rules of the game: Ed draws a sequence of balls at random (without replacement). After drawing each ball, Ed opens it and looks at the amount written on the check. He then must decide whether to keep the check and stop playing, or burn the check and draw another ball from the bucket. Suppose Ed has drawn k balls. He has just read the amount on the kth check and it is larger than those on the previous 19 1 checks (which Ed has already burned). Given this, what is the probability that Ed has drawn the check worth the largest amount of money in the entire bucket