In the 2006 federal election, the Liberal government that decriminalized the possession of small quantities of marijuana was replaced by a Conservative government. The new government considered modifying the Liberal legislation. In 2007, Angus Reid conducted a survey of 1028 adult Canadians, finding that 55% supported legalization of marijuana. The percentage of support was different among supporters of the three major political parties, as indicated in the table. For instance, 39% of Conservative voters supported the legalization of marijuana. Out of the 1028 people surveyed, the percentages of Conservative, Liberal, and NDP voters were 44%, 31%, and 25%, respectively.
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a) Convert the table into a contingency table in which the response percentages add to 100%.
b) What is the probability that a Liberal voter opposed the legalization of marijuana?
c) What is the probability that someone who supported the legalization of marijuana was an NDP voter?
d) Draw a probability tree in which the first branch gives the voting split and the second gives the opinion on legalizing marijuana. You don’t need to include the people who were “not sure.”
e) Often people are unwilling to disclose their voting preference. Let’s investigate whether we can use someone’s opinion on marijuana to predict his or her voting preference. From this survey, we know that the probability of someone being a Conservative voter was 44% in 2007. Suppose we interviewed someone at random and found that he or she opposed the legalization of marijuana. What’s the probability that this person is a Conservative voter?