Consider the following experiment. We start with a standard deck of 52 cards. We repeatedly draw a card from the deck without replacement until we draw an Ace and then draw one additional card, also without replacement. (For example, we might draw K, 2, A, 3.) In each draw, the card is chosen uniformly at random from the remaining cards. We define the following random variables:

N = total number of cards that we draw

D = total number of diamond cards that we draw

A = total number of Ace cards that we draw

(a) Identify the sample space for this experiment.

(b) Consider the outcome corresponding to drawing K, 2, A, 3. Find N(), D(), A().

(c) Find the range of N, D, and A.

(d) Find the probability that we draw exactly 3 cards, i.e., Pr(N = 3).

(e) Find the probability that the last card is not an Ace given that we draw 3 cards in total, i.e., Pr("last card is not an Ace"|N = 3).