a cbs news poll involved a nationwide random sample of 651 adults, asked those adults affiliation (democrat…

a cbs news poll involved a nationwide random sample of 651 adults, asked those adults affiliation (democrat, republican or none) and their opinion of how the us economy was (better, getting worse or about the same). the results are shown in the table below.\n\n| | better | same | worse |\n|--|--|--|--|\n| republican | 38 | 104 | 44 |\n| democrat | 12 | 87 | 137 |\n| none | 21 | 90 | 118 |\n\nif we randomly select one of the adults who participated in this study, compute: (round places)\na. p(republican) =\nb. p(worse) =\nc. p(worse|republican) =\nd. p(republican|worse) =\ne. p(republican and worse) =

a cbs news poll involved a nationwide random sample of 651 adults, asked those adults affiliation (democrat, republican or none) and their opinion of how the us economy was (better, getting worse or about the same). the results are shown in the table below.\n\n| | better | same | worse |\n|--|--|--|--|\n| republican | 38 | 104 | 44 |\n| democrat | 12 | 87 | 137 |\n| none | 21 | 90 | 118 |\n\nif we randomly select one of the adults who participated in this study, compute: (round places)\na. p(republican) =\nb. p(worse) =\nc. p(worse|republican) =\nd. p(republican|worse) =\ne. p(republican and worse) =

Answer

Explanation:

Step1: Calculate total number of adults

The total number of adults is the sum of all values in the table. $38 + 104+44 + 12+87 + 137+21+90+118=651$.

Step2: Calculate P(Republican)

The number of Republicans is $38 + 104+44=186$. So $P(\text{Republican})=\frac{186}{651}\approx0.286$.

Step3: Calculate P(worse)

The number of people who think the economy is getting worse is $44 + 137+118 = 299$. So $P(\text{worse})=\frac{299}{651}\approx0.460$.

Step4: Calculate P(worse|Republican)

By the formula for conditional - probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, $P(\text{worse}\cap\text{Republican})=\frac{44}{651}$ and $P(\text{Republican})=\frac{186}{651}$. So $P(\text{worse}|\text{Republican})=\frac{44}{186}\approx0.237$.

Step5: Calculate P(Republican|worse)

$P(\text{Republican}\cap\text{worse})=\frac{44}{651}$ and $P(\text{worse})=\frac{299}{651}$. So $P(\text{Republican}|\text{worse})=\frac{44}{299}\approx0.147$.

Step6: Calculate P(Republican and worse)

The number of Republicans who think the economy is getting worse is 44. So $P(\text{Republican and worse})=\frac{44}{651}\approx0.068$.

Answer:

a. $0.286$ b. $0.460$ c. $0.237$ d. $0.147$ e. $0.068$