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 use the formula for conditional probability:

\[
P(\text{Movies} | \text{31–35}) = \frac{\text{Number of 31–35 year olds who like Movies}}{\text{Total number of 31–35 year olds}}
\]

From the table, we see that:

- The number of people aged 31–35 who like movies is 21.
- The total number of people aged 31–35 is 50.

Now, we can calculate the conditional probability:

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

Next, we convert this probability into a percentage:

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

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

\[
\boxed{42\%}
\]