The accompanying table shows, for credit-card holders with one to three cards, the joint probabilities for number of cards owned (X) and number of credit purchases made in a week (Y).

Number of Cards (X)

Number of Purchases in a Week (Y)

0 1 2 3 4 1 0.06 0.13 0.09 0.07 0.03 2 0.02 0.07 0.09 0.09 0.07 3 0.01 0.02 0.05 0.08 0.12

a. For a randomly chosen person from this group, what is the probability distribution for number of purchases made in a week?

b. For a person in this group who has three cards, what is the probability distribution for number of purchases made in a week?

c. Are number of cards owned and number of purchases made statistically independent?