Final answer:
The joint probability mass function of z and w involves determining the probabilities of drawing aces in specific orders without replacement, whereas the marginal probability mass function of w sums the probabilities of specific w outcomes over all possible z values.
Step-by-step explanation:
When two cards are randomly drawn without replacement from an ordinary deck of 52 playing cards, z is the number of aces obtained in the first draw, and w is the total number of aces obtained in both draws.
For example, to find P(z=0, w=1), we first consider that the probability of not drawing an ace on the first draw is 48/52, as there are 48 non-ace cards in the deck. Then, the second card drawn must be an ace, so the probability for that is 4/51. Therefore, P(z=0, w=1) = (48/52) * (4/51).