Question

A research poll asked 1737 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.

	Earth is warming	Not warming	Don't know (or refuse)	Total
Conservative Republican	0.07	0.12	0.04	0.23
Mod/Lib Republican	0.10	0.02	0.06	0.18
Mod/Cons Democrat	0.11	0.02	0.04	0.17
Liberal Democrat	0.29	0.03	0.10	0.42
Total	0.57	0.19	0.24	1

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

not mutually exclusive

mutually exclusive

b) 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)
c) 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)
d) 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)
e) Does it appear that whether or not a respondent believes the earth is warming is independent of their party ideology?

belief in global warming and party ideology are independent

belief in global warming and party ideology are dependent

f) 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)

Answer 1

a)

not mutually exclusive ; as they have common sample space probability of 0.29.

b)

probability that a randomly chosen respondent believes the earth is warming or is a liberal Democrat

=(0.57+0.42-0.29)=0.7

c)

probability that a randomly chosen respondent believes the earth is warming given that they are a liberal Democrat =0.29/0.42=0.6905

d)

probability that a randomly chosen respondent believes the earth is warming given that they are a conservative Republican =0.07/0.23=0.3043

e)

belief in global warming and party ideology are dependent

f)

probability that a randomly chosen respondent is a moderate/liberal Republican given that they do not believe that the earth is warming =(0.18-0.1)/(1-0.57)=0.1860