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 find the probability that a person spends their time going to the movies given that they are 31–35 years old, we need to use the data provided for that age group.

From the table:

- The total number of people aged 31–35 years old is 50.
- The number of people aged 31–35 who go to the movies is 21.

The probability can be calculated using the formula:

\[
P(\text{Movies} | \text{31-35}) = \frac{\text{Number of people aged 31-35 who like movies}}{\text{Total number of people aged 31-35}}
\]

Substituting the numbers:

\[
P(\text{Movies} | \text{31-35}) = \frac{21}{50}
\]

Now, to express this probability as a percentage:

\[
P(\text{Movies} | \text{31-35}) \times 100 = \left( \frac{21}{50} \right) \times 100 = 42\%
\]

Thus, the probability that a person spends their time going to the movies, given that they are 31–35 years old, is **42%**.