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Chapter 5: Q 84. (page 330)

Urban voters The voters in a large city are 40%white, 40%black, and 20%Hispanic. (Hispanics may be of any race in official statistics, but here we are speaking of political blocks.) A mayoral candidate anticipates attracting 30%of the white vote, 90%of the black vote, and 50%of the Hispanic vote. Draw a tree diagram to represent this situation. What percent of the overall vote does the candidate expect to get? Use the four-step process to guide your work.

Short Answer

Expert verified

The probability of support for each political book is 58%

Step by step solution

01

Step 1. Given Information

In a major city, 40 percent of white voters, 40 percent black voters, and 20% Hispanic voters make up the voting population.

02

Step 2. Concept Used

Conditional probability: P(A鈭�B)=P(A/B)脳P(B)

03

Step 3. Calculation

The tree diagram is shown below, according to the question:

Now we must determine the likelihood of support for each political book.

P(white鈭�Support)=P(Support/white)脳P(white)=40%脳30%=0.40脳0.30=0.12P(Black鈭�Support)=P(Support/Black)脳P(Black)=40%脳30%=0.40脳0.90=0.36

P(Hispanic鈭�Support)=P(Support/Hispanic)脳P(Hispanic)=20%脳50%

Fill in the blanks with the corresponding probabilities:

P(Support)=0.1200+0.3600+0.1000=0.5800=58%

As a result, any political book has a 58% chance of being supported.

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