To find the probability that a person spends their time going to the movies given that they are 31–35 years old, we can use the following formula for conditional probability:
\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]
where:
- \(P(A|B)\) is the probability of event A occurring given event B is true.
- \(P(A \cap B)\) is the probability of both events A and B occurring.
- \(P(B)\) is the probability of event B occurring.
In this scenario:
- Event A: Spending time going to the movies.
- Event B: Being 31–35 years old.
From the table, we can see the data for people aged 31–35:
- Total people aged 31–35: 50
- People aged 31–35 who like going to the movies: 21
Now, we can find the conditional probability:
\[ P(\text{Movies} | 31–35) = \frac{\text{Number of people aged 31–35 who like Movies}}{\text{Total number of people aged 31–35}} = \frac{21}{50} \]
Now, we convert this to a percentage:
\[ P(\text{Movies} | 31–35) = \frac{21}{50} \times 100% \]
Calculating this gives:
\[ \frac{21}{50} = 0.42 \] \[ 0.42 \times 100% = 42% \]
Therefore, the probability that a person spends their time going to the movies, given that they are 31–35 years old, is:
\[ \boxed{42%} \]