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 answer

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 information provided in the table.

From the table, we see the following for the 31-35 years old age group:

  • Number of people who like going to the movies: 21
  • Total number of people in the 31-35 years old age group: 50

The probability \( P(\text{Movies} | \text{31-35}) \) 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 values:

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

To express this probability as a percentage, we multiply by 100:

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

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