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.

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:

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

From the table, we can extract the necessary values:

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

Now we calculate the probability:

\[
P(\text{Movies and 31-35}) = \text{Number of people aged 31-35 who like movies} = 21
\]

\[
P(\text{31-35}) = \text{Total number of people aged 31-35} = 50
\]

Now we plug these values into the conditional probability formula:

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

Now we convert this fraction 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:

\[
\boxed{42}
\]