Use the table to answer the question.

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 can use the following formula for conditional probability:

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

From the table, we see that there are 21 people aged 31–35 who like going to the movies, and the total number of people aged 31–35 is 50.

So, we have:

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

Now, we convert this probability into a percentage:

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

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