(p. 164). Recall that the total number of employees aged 15–74 years decreased from 2019 to 2020 and the number of self-employed people decreased by about 1%. Suppose in 2020, the population aged 15 to 74 is divided into three groups so that the first group has persons aged 15 to 34, the second group has persons aged 35 to 54, and the third group has persons aged 55 to 74. Probability distributions of partnerships for each group are determined. The set of distributions is as follows (probabilities in parentheses). Group 1: 0 partnership (.15), 2 partnerships (.15), 4 partnerships (.35), 6 partnerships (.05), 8 or more partnerships (.3); Group 2: 0 partnership (.14), 2 partnerships (.3), 4 partnerships (.35), 6 partnerships (.2), 8 or more partnerships (.01); Group 3: 0 partnership (.2), 2 partnerships (.4), 4 partnerships (.25), 6 partnerships (.1), 8 or more partnerships (.05).

a. Verify that the properties of a discrete probability distribution are satisfied for the number of partnerships in Group 1.

b. Repeat part a for the number of partnerships in Groups 2 and 3.

c. Find the probability that the number of partnerships in Group 1 will exceed 3.

d. Repeat part c for the number of partnerships in Groups 2 and 3.