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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 candidate expects to receive 58% of the total vote.

Step by step solution

01

Identify Voter Blocks

Determine the percentage of each racial group within the voters: 40% are white, 40% are black, and 20% are Hispanic. This forms the basis of our voter calculation.
02

Calculate Expected Votes from Each Group

Calculate the percentage of votes the candidate expects from each group: 30% of the white vote, 90% of the black vote, and 50% of the Hispanic vote. Multiply each group's voter percentage by the expected vote percentage for that group.
03

Draw the Tree Diagram

Create a tree diagram starting from the initial voter population. Split the tree into the three racial groups (40% white, 40% black, and 20% Hispanic). From each group, draw branches to show the support percentage (e.g., from white, a 30% branch towards support and 70% against).
04

Calculate Total Expected Vote

Calculate the total expected vote by adding together the contributions from each group: \(0.4 \times 0.3 = 0.12\) from whites, \(0.4 \times 0.9 = 0.36\) from blacks, and \(0.2 \times 0.5 = 0.10\) from Hispanics. Sum these values to find the overall expected vote percentage.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Voter Demographics
Understanding voter demographics is crucial for predicting electoral outcomes. In our city example, voters are categorized into three racial groups: white, black, and Hispanic. These groups account for 40%, 40%, and 20% of the city's population, respectively.
  • Demographics provide insight into the population composition.
  • They help in identifying potential voting patterns.
  • The distribution of these groups forms the base for any further analysis.
Assessing demographics enables candidates to tailor their approach and message. It helps to gauge which voter blocks are likely to support them and to what extent.
Probability Calculations
Probability plays a major role in predicting election outcomes. In this context, it involves calculating the likelihood of receiving votes from each demographic group. Begin by determining the percentage of expected support from each group:
  • 30% of the white vote
  • 90% of the black vote
  • 50% of the Hispanic vote
These probabilities reflect the candidate鈥檚 anticipated popularity within each group. By calculating the expected number of votes from each group, we derive insight into the potential total support base.To calculate the expected votes from a group, multiply the group's size by the probability of the candidate receiving their votes. For instance, for the white voters: \[ 0.4 \times 0.3 = 0.12 \] This calculation shows that 12% of the total voter population is expected to come from white voters supporting the candidate.
Political Statistics
Political statistics are essential for making informed decisions about campaign strategies. They cover various aspects like voter turnout, support levels, and demographic influences.
  • They help to quantify how demographics impact elections.
  • Provide data-driven insights for strategic decision-making.
For our candidate, political statistics regarding expected votes from different groups help assess the campaign鈥檚 viability. By summing up the contributions from each group:
  • 12% from white voters
  • 36% from black voters
  • 10% from Hispanic voters
Adding these, 58% of the total voter population is expected to support the candidate. Such calculations exemplify the power of statistics in political strategy.
Racial Group Percentages
Racial group percentages play a pivotal role in understanding voting dynamics within a city. These percentages are determined through demographic surveys and historical data analysis. For political campaigns, knowing the percentage of each racial group in the voter's pool helps in resource allocation and messaging tactics.
  • 40% white voters
  • 40% black voters
  • 20% Hispanic voters
Each percentage reflects the potential impact of that group within the electoral process. Understanding these divisions allows candidates to target their efforts effectively. In our example, the data indicates balanced weights between white and black voters, with a smaller percentage for Hispanics. Acknowledging these differences allows for strategic emphasis on high-support areas, thereby maximizing the chances of electoral success.

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