The residents of a small town and the surrounding area are divided over the proposed construction of a sprint car racetrack in the​ town, as shown in the table on the right.
Support
Racetrack
Oppose Racetrack
Live in Town
2 comma 754
878
Live in Surrounding Area
4 comma 309
1 comma 140
If a newspaper reporter randomly selects a person to interview from these​ people,
a. what is the probability that the person supports the​ racetrack?
b. what are the odds in favor of the person supporting the​ racetrack?


We are given a table showing the distribution of people who either support or oppose a racetrack based on their location (town or surrounding area). The numbers in the table are as follows:

|                      | Support Racetrack | Oppose Racetrack |
|----------------------|------------------|-----------------|
| **Live in Town**      | 2,754            | 878             |
| **Live in Surrounding Area** | 4,309            | 1,140           |

### a. Probability that the person supports the racetrack

The probability that a person supports the racetrack is given by the ratio of the number of people who support the racetrack to the total number of people. First, we compute the total number of people who support the racetrack and the total number of people.

- Total number of people who support the racetrack:
  \[
  2,754 + 4,309 = 7,063
  \]
  
- Total number of people (supporters + opponents):
  \[
  2,754 + 878 + 4,309 + 1,140 = 9,081
  \]

Now, the probability \(P(\text{Support})\) is:
\[
P(\text{Support}) = \frac{\text{Number of supporters}}{\text{Total number of people}} = \frac{7,063}{9,081} \approx 0.7775
\]

So, the probability that a randomly selected person supports the racetrack is approximately **0.7775**, or **77.75%**.

### b. Odds in favor of the person supporting the racetrack

The odds in favor of an event is the ratio of the number of favorable outcomes to the number of unfavorable outcomes.

- Number of favorable outcomes (supporters): \(7,063\)
- Number of unfavorable outcomes (opponents): \(878 + 1,140 = 2,018\)

The odds in favor of the person supporting the racetrack is:
\[
\text{Odds} = \frac{\text{Number of supporters}}{\text{Number of opponents}} = \frac{7,063}{2,018} \approx 3.5
\]

So, the odds in favor of the person supporting the racetrack are approximately **3.5:1**.

### Summary:
- **a.** The probability that a randomly selected person supports the racetrack is **0.7775** or **77.75%**.
- **b.** The odds in favor of the person supporting the racetrack are approximately **3.5:1**.

Do you want more details or have any questions?

Here are 5 related questions for practice:
1. What is the probability that a randomly selected person opposes the racetrack?
2. What are the odds against the person supporting the racetrack?
3. What is the probability that a randomly selected person lives in the town?
4. What is the probability that a person who opposes the racetrack lives in the surrounding area?
5. If two people are selected at random, what is the probability that both support the racetrack?

**Tip:** When calculating probabilities and odds, always make sure to carefully distinguish between favorable and unfavorable outcomes to avoid confusion.

The residents of a small town and the surrounding area are divided over the proposed construction of a sprint car racetrack in the town. What is the probability that a randomly selected person supports the racetrack? What are the odds in favor of the person supporting the racetrack?

Calculate the probability and odds in favor of supporting a racetrack in a small town. Learn step-by-step how to determine the probability that a randomly selected person supports the racetrack and the odds in favor of support based on population data. Suitable for high school students learning basic probability and statistics.

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