Question

section 5.4 homework score: 2.2/14 answered: 3/14 question 3 score on last try: 0.2 of 1 pts. see details for more. at least one scored part is incorrect. jump to first changeable incorre > next question get a similar question you can retry this a cbs news poll involved a nationwide random sample of 651 adults, ask affiliation (democrat, republican or none) and their opinion of how the better, getting worse or about the same). the results are shown in the

	better	same	worse
democrat	12	87	137
none	21	90	118

if we randomly select one of the adults who participated in this study, co places) a. p(republican) = 0.286 × enter an integer or decimal number, accurate to at least 4 decimal pla b. p(worse) = 0.460 × c. p(worse|republican) = 0.237 × d. p(republican|worse) = 0.147 √ e. p(republican and worse) = 0.088 ×

Explanation:

Step1: Calculate total number of participants

The total number of participants is \(38 + 104+44 + 12+87+137+21+90+118=651\).

Step2: Calculate \(P(\text{Republican})\)

The number of Republicans is \(38 + 104+44 = 186\). So \(P(\text{Republican})=\frac{186}{651}\approx0.2857\).

Step3: Calculate \(P(\text{worse})\)

The number of people who think it is getting worse is \(44 + 137+118=299\). So \(P(\text{worse})=\frac{299}{651}\approx0.4624\).

Step4: Calculate \(P(\text{worse}|\text{Republican})\)

By the formula of conditional - probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\), and \(P(\text{worse}\cap\text{Republican})=\frac{44}{651}\), \(P(\text{Republican})=\frac{186}{651}\), then \(P(\text{worse}|\text{Republican})=\frac{44}{186}\approx0.2366\).

Step5: Calculate \(P(\text{Republican and worse})\)

The number of Republicans who think it is getting worse is 44. So \(P(\text{Republican and worse})=\frac{44}{651}\approx0.0676\).

Answer:

a. \(0.2857\)
b. \(0.4624\)
c. \(0.2366\)
e. \(0.0676\)