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:
-
Identify the total number of voters:
The total number of registered voters in the survey is 3,228. -
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. -
Calculate the probability:
The probability that a randomly chosen voter is between 39 and 49 years old and is a Democrat can be calculated using the formula:Plugging in the numbers:
Now, we calculate this fraction:
Rounding this to the nearest hundredth gives:
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:
- What is the probability that a randomly chosen voter is registered as a Republican?
- How many voters are there in total for each age group?
- What is the proportion of Independents among the total voters?
- What is the probability of selecting a voter who is either a Democrat or an Independent?
- 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
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