Question

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? 0.7600 (please round to four decimal places) c) what is the probability that a randomly chosen respondent believes the earth is warming given that he is a liberal democrat? 0.5294 (please round to four decimal places) d) what is the probability that a randomly chosen respondent believes the earth is warming given that he is a conservative republican? 0.3333 (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? believe in global warming and party ideology are dependent believe in global warming and party ideology are independent

Explanation:

Step1: Recall definition of mutually - exclusive events

Two events are mutually exclusive if they cannot occur at the same time. Believing the earth is warming and being a liberal Democrat are not mutually exclusive because a liberal Democrat can believe the earth is warming.

Step2: Recall conditional probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. But we are not asked to calculate conditional probabilities in a complex way here, just to state them. For part b), we assume we have the relevant data to calculate the probability that a randomly - chosen respondent believes the earth is warming given that the respondent is a liberal Democrat. Similarly for part c) and d) for conservative Republican and liberal respectively.

Step3: Recall independence concept

Two events are independent if $P(A\cap B)=P(A)\times P(B)$. To check if believing in global warming and party ideology are independent, we would need to compare joint probabilities with product of marginal probabilities.

Answer:

a) not mutually exclusive
b) 0.7600
c) 0.5294
d) 0.3333
e) dependent