4.184, Governors. The National Governors Association publishes data on U.S. gove
ID: 3226042 • Letter: 4
Question
4.184, Governors. The National Governors Association publishes data on U.S. governors in Governors’ Political Affiliations & 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
50
Two U.S. governors are selected at random without replacement.
a. Find the probability that the first is a Republican and the second a Democrat.
b. Find the probability that both are Republicans
c. Draw a tree diagram
d. What is the probability that the two governors selected have the same political- party affiliation?
e. What it the probability that the two governors selected have different political-party affiliations?
Party
Frequency
Democratic
20
Republican
30
50
Explanation / Answer
a)
probability that the first is a Republican and the second a Democrat =
= 30/50(probability of being a republican) * 20/49(probability of being a democrat after one republican is taken out)
= 0.24489
b)
probability that both are Republicans = 30/50 * 29/49 = 0.3551
c)
probability that the two governors selected have the same political- party affiliation =
it mean that both are either of democrat or republic.
probability that both are Republicans = 0.3551 (calculated in above question)
probability that both are democrats = 20/50 * 19/49 = 0.1551
therefore probability that the two governors selected have the same political- party affiliation = 0.1551 + 0.3551 = 0.5102
d)
probability that the two governors selected have different political-party affiliations =
=1 - probability that the two governors selected have the same political- party affiliation
= 1 - 0.5102 = 0.4898
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