Question

a recent poll of americans was used to present the public’s opinions concerning the death penalty. the question asked was, “are you in favor of the death penalty for someone convicted of murder?” the table below lists the results of the poll based on where each person lives. use the information in this table for problems 21 to 26.

	approve	disapprove	no opinion	total
south	165	70	15	250
west	168	95	11	274
midwest	211	90	16	317
total	715	375	50	1140

1. if a survey participant is selected at random, what is the probability that the respondent approves of the death penalty?
2. if a survey participant is selected at random, what is the probability that the respondent has no opinion about the death penalty?
3. if a survey participant is selected at random, what is the probability that the respondent is from the east or the south?
4. if a survey participant is selected at random, what is the probability that the respondent is from the midwest or the west?
5. if a survey participant is selected at random, what is the probability that the respondent is from the south or disapproves of the death penalty?
6. if a survey participant is selected at random, what is the probability that the respondent is from the west or approves of the death penalty?

Explanation:

Problem 21

Step1: Identify favorable and total outcomes

Favorable (approve): 715, Total: 1140

Step2: Calculate probability

Probability = $\frac{715}{1140}$ = Simplify by dividing numerator and denominator by 5: $\frac{143}{228}$ ≈ 0.627

Step1: Identify favorable and total outcomes

Favorable (no opinion): 50, Total: 1140

Step2: Calculate probability

Probability = $\frac{50}{1140}$ = Simplify by dividing numerator and denominator by 10: $\frac{5}{114}$ ≈ 0.0439

Step1: Identify counts for East, South, and total

East total: 299, South total: 250, Total: 1140. No overlap (mutually exclusive).

Step2: Apply addition rule for mutually exclusive events

Probability = $\frac{299 + 250}{1140}$ = $\frac{549}{1140}$ = Simplify by dividing numerator and denominator by 3: $\frac{183}{380}$ ≈ 0.4816

Answer:

$\frac{143}{228}$ (or approximately 0.627)

Problem 22