(p. 220). It considers self-employed workers grouped by age and the number of part-timers they employ. Groups 1, 2, and 3 are for self-employed INVIQ workers aged 15 to 34, 35 to 54, and 55 to 74, respectively. Recall the proportions for each group is as follows (probabilities in parentheses). Group 1: zero partnership (0.15), 2 partnerships (0.15), 4 partnerships (0.35), 6 partnerships (0.05), 8 or more partnerships (0.3); Group 2: zero partnership (0.14), 2 partnerships (0.3), 4 partnerships (0.35), 6 partnerships (0.2), 8 or more partnerships (0.01); Group 3: zero partnership (0.2), 2 partnerships (0.4), 4 partnerships (0.25), 6 partnerships (0.1), 8 or more partnerships (0.05). Let x represent the number of partnerships.

a. List the possible values of x.

b. Find P1x = 42. [Hint: The event 5x = 46 is the union of the events 5x = 4 in Group 16, 5x = 4 in Group 26, and 5x = 4 in Group 36. Also, P1x = 4 in Group 12 = P1x = 4 | Group 12 * P(Group 1), where P(Group 1) = 1>3, since the groups are of equal size.]

c. Find the probability distribution for x.

d. What is the probability that the self-employed will have at least 6 partnerships?