Math Problem Statement

A survey showed the following information on the ages and party affiliations of registered voters in a certain city.

Age Republican Democrat Independent Other Total 18–28

205

432

98

112

847

29–38

311

301

109

83

804

39–49

250

251

150

122

773

≥ 50

272

283

142

107

804

Total

1,038

1,267

499

424

3,228

Compute the probability that a randomly chosen voter from the survey will satisfy the following. Round to the nearest hundredth.

The voter is between 39 and 49 and is registered as a Democrat.

Solution

To compute the probability that a randomly chosen voter from the survey is between 39 and 49 years old and is registered as a Democrat, we can use the following steps:

  1. Identify the total number of voters:
    The total number of registered voters in the survey is 3,228.

  2. Identify the number of voters between 39 and 49 who are Democrats:
    From the table, the number of voters in the age group 39–49 who are Democrats is 251.

  3. Calculate the probability:
    The probability PP that a randomly chosen voter is between 39 and 49 years old and is a Democrat can be calculated using the formula:

    P(39-49 and Democrat)=Number of 39-49 DemocratsTotal number of votersP(\text{39-49 and Democrat}) = \frac{\text{Number of 39-49 Democrats}}{\text{Total number of voters}}

    Plugging in the numbers:

    P(39-49 and Democrat)=2513228P(\text{39-49 and Democrat}) = \frac{251}{3228}

    Now, we calculate this fraction:

    P(39-49 and Democrat)0.0777P(\text{39-49 and Democrat}) \approx 0.0777

    Rounding this to the nearest hundredth gives:

    P0.08P \approx 0.08

Thus, the probability that a randomly chosen voter is between 39 and 49 years old and is registered as a Democrat is approximately 0.08.

Do you want details or have any questions?

Here are some related questions you might consider:

  1. What is the probability that a randomly chosen voter is registered as a Republican?
  2. How many voters are there in total for each age group?
  3. What is the proportion of Independents among the total voters?
  4. What is the probability of selecting a voter who is either a Democrat or an Independent?
  5. How do these probabilities change if we consider only the age group of 29-38?

Tip: When calculating probabilities, always make sure your total is correct to ensure accurate results.

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Math Problem Analysis

Mathematical Concepts

Probability
Statistics

Formulas

P(A) = Number of favorable outcomes / Total number of outcomes

Theorems

Basic Probability Theory

Suitable Grade Level

Grades 9-12