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Let's analyze and solve this problem step by step.

### Given Data:
- Total boys who play sports = 108
- Boys who play football = 36
- Boys who run track = 38
- Boys who play both football and run track = 15

### 1. **P(boy plays football):**
The probability of a boy playing football is the number of boys who play football divided by the total number of boys:

\[
P(\text{boy plays football}) = \frac{36}{108} = 0.3333 \approx 33\%
\]

### 2. **P(boy does not play football):**
The probability of a boy not playing football is:

\[
P(\text{boy does not play football}) = 1 - P(\text{boy plays football}) = 1 - 0.3333 = 0.6667 \approx 67\%
\]

### 3. **P(boy plays football OR track):**
Using the addition rule for probabilities:

\[
P(\text{football OR track}) = P(\text{football}) + P(\text{track}) - P(\text{football AND track})
\]

Where:
- \(P(\text{football}) = \frac{36}{108} = 0.3333\)
- \(P(\text{track}) = \frac{38}{108} = 0.3519\)
- \(P(\text{football AND track}) = \frac{15}{108} = 0.1389\)

Now apply the formula:

\[
P(\text{football OR track}) = 0.3333 + 0.3519 - 0.1389 = 0.5463 \approx 55\%
\]

### Final Answers:
1. P(boy plays football) = **33%**
2. P(boy does not play football) = **67%**
3. P(boy plays football OR track) = **55%**

---

Would you like further details or explanations? Here are some follow-up questions to deepen your understanding:

1. How do you find the probability of two events happening simultaneously?
2. What is the general formula for calculating the union of two probabilities?
3. Can you explain why we subtract \(P(\text{football AND track})\) in the third calculation?
4. How does the complement rule help in calculating \(P(\text{boy does not play football})\)?
5. What is the significance of rounding probabilities to whole percentages?

**Tip:** Always check if events are mutually exclusive before applying the addition rule for probabilities.

Spencer high school has 108 boys who play sports. 36 play football, 25 run cross country, 22 play basketball, 35 play baseball, and 38 run track. There are 15 boys who play football and run track. Find the following probabilities, round to whole percent.

1. P(boy plays football) = ______ %
2. P(boy does not play football) = ______ %
3. P(boy plays football OR track) = ______ % [show the steps of the addition rule]

Learn how to calculate probabilities for sports participation at Spencer High School. Understand the probability of playing football, not playing football, or participating in football or track. This problem covers key probability concepts and is suitable for students in Grades 9-10.

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