wendy45cinto
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A CBS News poll involved a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.

better same worse
Republican 38 104 44
Democrat 12 87 137
none 21 90 118
If we randomly select one of the adults who participated in this study, compute: (round to four decimal places)

a.P(Republican) =

b.P(better) =

c.P(better|Republican) =

d.P(Republican|better) =

e.P(Republican and better) =

Respuesta :

MrRoyal

Answer:

[tex]P(Republican) = 0.2857[/tex]

[tex]P(Better) = 0.1091[/tex]

[tex]P(better | Republican) = 0.2043[/tex]

[tex]P(Republican | better) = 0.5352[/tex]

[tex]P(Republican\ n\ Better) = 0.0584[/tex]

Step-by-step explanation:

Given

---------------------better same worse

Republican ------38 -----104 --- 44

Democrat --------12 -------87 --- 137

None --------------21 --------90 ----118

[tex]Total = 651[/tex]

Solving (a): P(Republican)

Here, we consider the "republican" row only;

[tex]n(Republican) = 38 + 104 + 44[/tex]

[tex]n(Republican) = 186[/tex]

[tex]P(Republican) = \frac{n(Republican)}{Total}[/tex]

[tex]P(Republican) = \frac{186}{651}[/tex]

[tex]P(Republican) = 0.2857[/tex]

Solving (b): P(Better)

Here, we consider the "better" column only

[tex]n(Better) = 38 + 12+21[/tex]

[tex]n(Better) = 71[/tex]

[tex]P(Better) = \frac{n(Better)}{Total}[/tex]

[tex]P(Better) = \frac{71}{651}[/tex]

[tex]P(Better) = 0.1091[/tex]

Solving (c): P(better | Republican)

This is calculated as:

[tex]P(better | Republican) = \frac{P(better\ n\ Republican)}{P(Republican)}[/tex]

For, P(better n Republican), we consider the cell where "Better" and "Republican" intersects;

i.e. [tex]n(Better\ n\ Republican) = 38[/tex]

[tex]P(Better\ n\ Republican) = \frac{38}{651}[/tex]

So:

[tex]P(better | Republican) = \frac{P(better\ n\ Republican)}{P(Republican)}[/tex]

[tex]P(better | Republican) = \frac{38}{651}/\frac{186}{651}[/tex]

[tex]P(better | Republican) = \frac{38}{651} * \frac{651}{186}[/tex]

[tex]P(better | Republican) = \frac{38}{186}[/tex]

[tex]P(better | Republican) = 0.2043[/tex]

Solving (d): P(Republican | better)

This is calculated as:

[tex]P(Republican | better) = \frac{P(Republican\ n\ better)}{P(better)}[/tex]

[tex]P(Republican\ n\ Better) =P(Better\ n\ Republican) = \frac{38}{651}[/tex]

So:

[tex]P(Republican | better) = \frac{P(Republican\ n\ better)}{P(better)}[/tex]

[tex]P(Republican | better) = \frac{38}{651}/\frac{71}{651}[/tex]

[tex]P(Republican | better) = \frac{38}{651} * \frac{651}{71}[/tex]

[tex]P(Republican | better) = \frac{38}{71}[/tex]

[tex]P(Republican | better) = 0.5352[/tex]

Solving (e): P(Republican and better)

[tex]P(Republican\ n\ Better) =P(Better\ n\ Republican) = \frac{38}{651}[/tex]

[tex]P(Republican\ n\ Better) = 0.0584[/tex]

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