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) 0 NUMBER OF PURCHASES IN WEEK (Y) 1 2 3 4 .08 .13 .09 .03 08 .08 .01 03 .06 888 .06 .09 .08 .08 358 03 07

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

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

(c) Are the number of cards owned and number of purchases made statistically indepen- dent?