Question

Use the table to answer the question.

Bowling Dancing Movies Total
20–25 Years Old 15 13 12 40
26–30 Years Old 12 10 8 30
31–35 Years Old 18 11 21 50
Total 45 34 41 120
In a survey, 120 people are asked how they like to spend their free time. Their responses are recorded on the table based on their age. What is the probability that a person spends their time going to the movies, given that they are 31–35 years old? Express your answer as a percentage, rounded to the nearest whole number.

(1 point)
%

Answer 1

To calculate the probability that a person spends their time going to the movies given that they are 31–35 years old, we will use the following formula for conditional probability:

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

In this context:
- \(A\) is the event that a person spends time going to the movies.
- \(B\) is the event that a person is 31–35 years old.

From the table, we find the number of people who are 31–35 years old and go to the movies:

- The number of people aged 31–35 who go to the movies is 21.

The total number of people aged 31–35 is:

\[
18 \text{ (Bowling)} + 11 \text{ (Dancing)} + 21 \text{ (Movies)} = 50
\]

Now we can calculate the probability that a person spends their time going to the movies given that they are 31–35 years old:

\[
P(\text{Movies} | 31-35) = \frac{\text{Number of people aged 31–35 who go to the movies}}{\text{Total number of people aged 31–35}} = \frac{21}{50}
\]

Now convert this fraction into a percentage:

\[
\frac{21}{50} \times 100 = 42\%
\]

Therefore, the probability that a person spends their time going to the movies, given that they are 31–35 years old, is

\[
\boxed{42\%}
\]