1. A Gallup survey asks 1,500 Americans about their views regarding Legalization of Marijuana. The table below shows the proportions of responses by political ideology and whether they Favor or Oppose legalizing marijuana:

Favor Legalization	Oppose Legalization	Total
	Conservatives	0.159	0.214	0.373
Political	Moderates	0.258	0.095	0.353
Ideology	Liberals	0.216	0.058	0.274
	Total	0.633	0.367	1.000

1. Are favoring legalization and being a liberal mutually exclusive?

Since favoring and liberal are not equal 0 they are not mutually exclusive

1. What is the probability that a randomly chosen respondent favors legalization or is a liberal?

The proportion of respondents that favors the legalization of marijuana = 0.633

The proportion of respondents that are liberals = 0.274

The proportion of respondents that favors the legalization of marijuana and are liberals = 0.216

P(favors legalization or is a liberal) = 0.633 + 0.274 - 0.216

P(favors legalization or is a liberal) = 0.691

Therefore, the probability that a randomly chosen respondent favors legalization or is a liberal is0.691.

1. What is the probability that a randomly chosen respondent favors legalization given that he/she is a liberal?

The probability that a randomly chosen respondent favors legalization given that he/she is a liberal is equal to the proportion of respondents that favors the legalization of marijuana and are liberals divided by the proportion of respondents that are liberals.

P(favors legalization given that he/she is a liberal) = 0.216 / 0.274

P(favors legalization given that he/she is a liberal) = 0.788

Therefore, the probability that a randomly chosen respondent favors legalization given that he/she is a liberal is 0.788.

1. What is the probability that a randomly chosen respondent favors legalization given that he/she is a conservative?

The probability that a randomly chosen respondent favors legalization given that he/she is a conservative is equal to the proportion of respondents that favors the legalization of marijuana and are conservative divided by the proportion of respondents that are conservative.

Based on the table, here are the proportions of the following.

The proportion of respondents that favors the legalization of marijuana and are conservative = 0.159

The proportion of respondents that are conservative = 0.373

P(favors legalization given that he/she is a conservative) = 0.159 / 0.373

P(favors legalization given that he/she is a conservative) = 0.426

Therefore, the probability that a randomly chosen respondent favors legalization given that he/she is a conservative is 0.426.

1. Is whether or not a respondent favors legalization independent of their political ideology? Explain your answer.
2. What is the probability that a randomly chosen respondent is a moderate given that he/she favors legalization?