Public Policy and Political Science Recent national election

Public Policy and Political Science. Recent national elections suggest that the political ideology of adults in the United States is very evenly divided. In a USA Today/Gallup survey, 29% were Republicans, 30% were Democrats, and 41% were Independents. In addition, 51% of all Republicans, 16% of all Democrats, and 28% of all Independents describe their political views as conservative. Suppose an adult in the United States is selected at random.

(a) What is the probability (± 0.0001) that the adult is a Republican and describes her political views as conservative?

P(RC) =

(b) What is the probability (± 0.0001) that the adult is a Democrat and describes his political views as conservative?

P(DC) =

(c) Suppose the adult described his views as conservative.

What is the probability (± 0.0001) that he is an Independent?

P(I|C) =

Marketing and Consumer Behavior. Americans drink a lot of coffee, and they put all sorts of extras into their coffee to enhance the drink, including flavor shots and flavored creams. Research data indicates that 62% of all coffee drinkers put creamer in their coffee. Of those people who use creamer, 40% say they would drink more coffee if their preferred flavors were offered.

Suppose a coffee drinker is selected at random

(a) Suppose the coffee drinker uses creamer. What is the probability (± 0.0001) hat he would not drink more even if his preferred flavor were offered?

P(M|C) =

(b) What is the probability (± 0.0001) that the coffee drinker uses creamer and would drink more if his preferred flavor were offered?

P(CM) =

(c) Suppose three coffee drinkers are selected at random. What is the probability (± 0.0001) that exactly one uses creamer?

P(1 of 3 uses creamer) =

Solution

the probability (± 0.0001) that the adult is a Republican and describes her political views as conservative

= P(R intersection C)

= P(R)P(C)
= 0.29(0.51)

= 0.1479

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b) the probability (± 0.0001) that the adult is a Democrat and describes his political views as conservative

= P(DC) =

= 0.30(0.16)

= 0.048

c) P(I/C) = P(IC)/P(C) = 0.41(0.28)/(0.29)(0.51)+0.30(0.16)+0.41(0.28)

= 0.3695

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a) P(M\'/C) = P(M\'C)/P(C)

= 60%(62%)/(60%(62%)+(62%)(40%)

= 0.60

b) P(CM) = 0.4(0.62)

=0.248

c) No of coffee drinkers who uses creamer is binomial with p = 0.4 and n =3

P(X=1) = 3C1(0.4)(0.6)²

= 3(0.4)(0.36)

=0.0432