- The National Governors Association publishes data on U.S. governors in Governors’ Political Affiliations and Terms of Office. Based on that document, we obtained the following frequency distribution for U.S. governors, as of 2013.
Party Frequency
Democratic 20
Republican 30
Two U.S. governors are selected at random without replacement.
a. Find the probability that the first is a Republican and the second is a Democrat.
b. Find the probability that both are Republican.
c. Draw a tree diagram for this problem.
d. What is the probability that the two governors selected have the same political-party affiliation?
e. What is the probability that the two governors selected have different political-party affiliation?
2. The U.S. National Science Foundation publishes data on doctoral degrees conferred in the document Science and Engineering Doctorate Awards. The following joint probability distribution summarizes the doctoral degrees conferred in the social sciences and psychology by gender during one year.
Field
Social science Psychology
F1 F2 P(Gi)
Male 0.300 0.119 0.419
G1
Gender Female 0.282 0.298 0.581
G2
P(Fj) 0.582 0.418 1.000
a. Find P(G1), P(F1), and P(G1 and F1).
b. Use the special multiplication rule to determine whether events G1 and F1 are independent.
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