To determine the probability that a randomly selected person is between 20 and 40 years old, we first need to find the total number of people attending the movies, as well as the number of people in the specified age range.
From the table, we can sum up the attendees for each age group across all three movies:
-
Action movie:
- Under 20: 10
- Between 20 and 40: 6
- Over 40: 16
- Total for Action: 10 + 6 + 16 = 32
-
Comedy movie:
- Under 20: 4
- Between 20 and 40: 17
- Over 40: 3
- Total for Comedy: 4 + 17 + 3 = 24
-
Drama movie:
- Under 20: 6
- Between 20 and 40: 18
- Over 40: 20
- Total for Drama: 6 + 18 + 20 = 44
Next, we can sum the total number of attendees from all three movies:
- Total attendees = Total for Action + Total for Comedy + Total for Drama
- Total attendees = 32 + 24 + 44 = 100
Now, we will find the total number of people who are between 20 and 40 years old across all movies:
- Between 20 and 40 for Action: 6
- Between 20 and 40 for Comedy: 17
- Between 20 and 40 for Drama: 18
Total between 20 and 40 = 6 + 17 + 18 = 41
Now we can calculate the probability:
\[ \text{Probability} = \frac{\text{Number of people between 20 and 40}}{\text{Total number of people}} = \frac{41}{100} = 0.41 \]
So, rounding to the nearest hundredth, the probability that the person selected is between 20 and 40 years old is:
0.41
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