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Two-Way Table Percentage Calculation: Conditional Probability
Published on March 4, 2026
Statistics
Calculate the conditional percentage of people in the 21-34 age bracket who prefer football using data from a two-way frequency table.
Question
Answer
Here is the step-by-step solution to the problem.
The question asks: “What percent of the people between the ages of 21 and 34 prefer football? Round your answer to the nearest whole number percent.”
This is a conditional probability problem based on the provided two-way table. We need to find the percentage of people who prefer football given that they are in the 21-34 age group.
Step 1: Identify the relevant data from the table.
First, locate the row corresponding to the age group “21-34”.
| Age Group | Basketball | Football | Soccer | Baseball | Row Total |
|---|---|---|---|---|---|
| 21-34 | 6 | 9 | 9 | 9 |
|
-
Number of people in the 21-34 age group (Total for the condition):
This is the sum of respondents in that row: -
Number of people between 21 and 34 who prefer Football (Favorable outcome):
From the table, the value at the intersection of the “21-34” row and the “Football” column is 9.
Step 2: Calculate the percentage.
The percentage is calculated using the formula:
Substitute the values:
Step 3: Simplify and convert to a decimal.
First, simplify the fraction
Now, convert the fraction to a decimal:
Convert to a percentage:
Step 4: Round to the nearest whole number percent.
We need to round
The percent of the people between the ages of 21 and 34 who prefer football is 27%.