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
10
10
20
Comedy
3
20
7
Drama
16
19
11
The manager is going to randomly select one person to win a free movie pass.
What is the probability that the person selected is 40 years old or younger? Round the answer to the nearest hundredth.

Answer 1

To find the probability that a randomly selected person is 40 years old or younger, we can start by calculating the total number of people in each age group for each movie category.

From the table, we have:

**Action Movie:**
- Under 20: 10
- Between 20 and 40: 10
- Over 40: 20
- **Total for Action:** 10 + 10 + 20 = 40

**Comedy Movie:**
- Under 20: 3
- Between 20 and 40: 20
- Over 40: 7
- **Total for Comedy:** 3 + 20 + 7 = 30

**Drama Movie:**
- Under 20: 16
- Between 20 and 40: 19
- Over 40: 11
- **Total for Drama:** 16 + 19 + 11 = 46

Next, we find the total number of people across all three movies:

\[
\text{Total} = 40 + 30 + 46 = 116
\]

Now, we calculate the number of people who are 40 years old or younger. This includes those under 20 and those between 20 and 40.

**Counting People 40 or Younger:**

**Action Movie:**
- Under 20: 10
- Between 20 and 40: 10
- **Total for Action (40 or younger):** 10 + 10 = 20

**Comedy Movie:**
- Under 20: 3
- Between 20 and 40: 20
- **Total for Comedy (40 or younger):** 3 + 20 = 23

**Drama Movie:**
- Under 20: 16
- Between 20 and 40: 19
- **Total for Drama (40 or younger):** 16 + 19 = 35

Now, add those totals together:

\[
\text{Total 40 or younger} = 20 + 23 + 35 = 78
\]

Now we can find the probability that a randomly selected person is 40 years old or younger:

\[
\text{Probability} = \frac{\text{Number of people 40 or younger}}{\text{Total number of people}} = \frac{78}{116}
\]

To calculate the probability:

\[
\frac{78}{116} \approx 0.6724137931
\]

Rounding to the nearest hundredth, we get:

\[
\text{Probability} \approx 0.67
\]

Thus, the probability that the person selected is 40 years old or younger is **0.67**.