Use the table to answer the question. Sports Preference Age Group Basketball Soccer Football Total 6–15 years old 4 37 9 50 16–25 years old 28 10 12 50 26–35 years old 3 6 41 50 Total 35 53 62 150 Given that someone prefers soccer, what is the probability that they are 26–35 years old? Express your answer as a percentage rounded to the nearest whole number. (1 point) %

1 answer

To find the probability that someone prefers soccer given that they prefer soccer, we first need to identify the total number of people who prefer soccer and how many of those are in the 26–35 years old age group.

From the table, the number of people who prefer soccer is:

  • 6–15 years old: 37
  • 16–25 years old: 10
  • 26–35 years old: 6

So, the total number of people who prefer soccer is:

\[ 37 + 10 + 6 = 53 \]

Next, we need to find the number of people in the 26–35 years old group who prefer soccer, which is 6.

The probability \( P \) that someone prefers soccer given that they are 26–35 years old is given by the formula:

\[ P(\text{26–35} | \text{soccer}) = \frac{\text{Number of people aged 26–35 who prefer soccer}}{\text{Total number of people who prefer soccer}} = \frac{6}{53} \]

Now, to express this as a percentage, we calculate:

\[ P(\text{26–35} | \text{soccer}) \times 100 = \left( \frac{6}{53} \right) \times 100 \approx 11.32 \]

Rounding to the nearest whole number gives us:

\[ \approx 11% \]

So, the final answer is:

11%