A research poll asked 1348 Americans \"From what you\'ve read and heard, is ther

Question

A research poll asked 1348 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) What is the probability that a randomly chosen respondent believes the earth is warming or is a liberal Democrat?  (please round to four decimal places)

b) What is the probability that a randomly chosen respondent believes the earth is warming given that they are a liberal Democrat?  (please round to four decimal places)

c) What is the probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican?  (please round to four decimal places)

d) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming?  (please round to four decimal places)

Conservative Republican Mod/Lib Republican Mod/Cons Democrat Liberal Democrat Total Earth is warming Not warmingDon't know (or refuse)Total 0.26 0.18 0.22 0.34 0.10 0.10 0.15 0.27 0.62 0.12 0.02 0.02 0.02 0.18 0.04 0.06 0.05 0.05 0.2

Explanation / Answer

a) P(earth is warming) = 0.62, P(Liberal democrat) =0.34 , P(earth is warming and is a Liberal democrat)= 0.27

P(earth is warming or is a liberal Democrat)= P(earth is warming) + P(Liberal democrat)- P(earth is warming and is a Liberal democrat)

=0.62+0.34-0.27=0.69

b) P(earth is warming|Liberal democrat) = P(earth is warming and is a Liberal democrat)/ P(Liberal democrat)

=0.27/0.34 =0.7941

c) P(earth is warming| conservative republican) = P(earth is warming and is a conservative republican)/ P(conservative republican)

= 0.1/0.26 =0.3846

d)

d) P(respondent is a moderate/liberal Republican | earth is not warming) =P(respondent is a moderate/liberal Republican and earth is not warming)/P(earth is not warming)

=0.02/0.18 =0.1111

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