Question

The table shows the ages of people attending three different movies in a movie theater.
Under 20 Between 20 and 40 Over 40
Action: 2,5,7
Comedy: 10,14,6
Drama: 12,3,3

The manager is going to randomly select one person to win a free movie pass.
What is the probability that the person's name that is selected is 40 years old or younger and watching the action movie? Round the answer to the nearest hundredth. Enter the answer in the box.

Answer 1

To find the probability that a randomly selected person is 40 years old or younger and watching the action movie, we first need to analyze the data provided in the table.

The ages for the Action movie are:
- Under 20: 2
- Between 20 and 40: 5
- Over 40: 7

**Total number of people watching Action movie:**
\[
2 + 5 + 7 = 14
\]

Now, we will find the number of people who are 40 years old or younger watching the Action movie. This includes those under 20 and those between 20 and 40.
- Under 20: 2
- Between 20 and 40: 5

**Total number of people 40 years old or younger watching Action:**
\[
2 + 5 = 7
\]

Next, we need to find the total number of people attending all three movies.

The data per movie is:
1. **Action**: 14
2. **Comedy**: 10 + 14 + 6 = 30
3. **Drama**: 12 + 3 + 3 = 18

**Total number of people in the theater:**
\[
14 + 30 + 18 = 62
\]

Now, we can calculate the probability that the selected person is 40 years old or younger watching the Action movie:
\[
P(\text{40 years old or younger and watching Action}) = \frac{\text{Number of people 40 years old or younger watching Action}}{\text{Total number of people}}
\]
\[
P = \frac{7}{62}
\]

Now, let's calculate this value:
\[
P \approx 0.1129032258
\]

Rounding to the nearest hundredth gives:
\[
P \approx 0.11
\]

So, the probability that the person's name that is selected is 40 years old or younger and watching the action movie is **0.11**.