Question

Question
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)
%

Answer 1

To find the probability that a person is aged 26–35 years old given that they prefer soccer, we can use the formula for conditional probability:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]

Where:
- \( A \) is the event that a person is aged 26–35 years old.
- \( B \) is the event that a person prefers soccer.

From the table, we have:
- The total number of people who prefer soccer (event \( B \)) is 53.
- The number of people who are 26–35 years old and prefer soccer (event \( A \cap B \)) is 6.

Now we can calculate \( P(A|B) \):

\[
P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{6}{53}
\]

Next, we convert this probability to a percentage:

\[
P(A|B) \times 100 = \left( \frac{6}{53} \right) \times 100 \approx 11.32
\]

Rounding to the nearest whole number gives us:

\[
\text{Probability} \approx 11\%
\]

Thus, the final answer is:

\[
\boxed{11}
\]