First, we need to determine the total number of people attending the movies. We will add up all the attendees for each type of movie.
For the Action movie:
- Under 20: 8
- Between 20 and 40: 5
- Over 40: 12
Total for Action = 8 + 5 + 12 = 25
For the Comedy movie:
- Under 20: 16
- Between 20 and 40: 11
- Over 40: 1
Total for Comedy = 16 + 11 + 1 = 28
For the Drama movie:
- Under 20: 10
- Between 20 and 40: 15
- Over 40: 9
Total for Drama = 10 + 15 + 9 = 34
Next, we calculate the total number of people attending any type of movie:
- Total people = Total for Action + Total for Comedy + Total for Drama
- Total people = 25 + 28 + 34 = 87
Now, we need to calculate the probability that a randomly selected person is watching the Drama movie. This probability is found by dividing the number of people watching Drama by the total number of people:
[tex]\[
\text{Probability of selecting a person watching Drama} = \frac{\text{Number watching Drama}}{\text{Total number of people}} = \frac{34}{87}
\][/tex]
Converting this fraction into a decimal:
[tex]\[
\frac{34}{87} \approx 0.39080459770114945
\][/tex]
Finally, we round this value to the nearest hundredth:
[tex]\[
0.39080459770114945 \approx 0.39
\][/tex]
So, the probability that the person selected is watching the Drama movie, rounded to the nearest hundredth, is [tex]\(0.39\)[/tex].
