A Pew Research poll asked 1,306 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies.

(a) Are believing that the earth is warming and being a liberal Democrat mutually exclusive?

(b) What is the probability that a randomly chosen respondent believes the earth is warming or is a liberal Democrat?

(c) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a liberal Democrat?

(d) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a conservative Republican?

(e) Does it appear that whether or not a respondent believes the earth is warming is independent of their party and ideology? Explain your reasoning.

(f) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that he does not believe that the earth is warming?

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Party and Ideology Conservative Republican Mod/Lib Republican Mod/Cons Democrat Liberal Democrat Total Earth is warming 0.11 0.06 0.25 0.18 0.60 Response Not warming 0.20 0.06 0.07 0.01 0.34 Don't Know Refuse 0.02 0.01 0.02 0.01 0.06 Total 0.33 0.13 0.34 0.20 1.00