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 answer

To find the probability that someone who prefers soccer is in the 26–35 years old age group, 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 in the 26–35 years old age group.
  • \(B\) is the event that a person prefers soccer.

From the table, we see the following information:

Number of people who prefer soccer:

  • Total people who prefer soccer: \(53\)

Number of people in the 26–35 years old age group who prefer soccer:

  • People aged 26–35 who prefer soccer: \(6\)

Now we can calculate the probability:

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

Next, we need to convert this probability into a percentage:

\[ \frac{6}{53} \approx 0.1132 \]

Converting this to a percentage:

\[ 0.1132 \times 100 \approx 11.32% \]

Finally, rounding to the nearest whole number gives us:

\[ \boxed{11%} \]