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**If a student is chosen at random, what is the probability that:**
*Round all answers to 3 decimal places as needed.*
**e) The student competed in Bachata or Bolero, but not FoxTrot?>**

To find the probability that a student competed in **Bachata or Bolero, but not FoxTrot**, we'll follow these steps:

### Step 1: Identify the regions in the Venn diagram for Bachata or Bolero but not FoxTrot.
- The Bachata set consists of the numbers 297, 360, and 272 (overlap with FoxTrot).
- The Bolero set consists of the numbers 330, 360, and 322 (overlap with FoxTrot).
- We **exclude** the regions where FoxTrot is involved, meaning we remove all numbers that intersect with FoxTrot (i.e., 272, 322, 312, and 289).

Thus, the relevant regions are:
- Bachata only: **297**
- Bolero only: **330**
- Bachata & Bolero (but not FoxTrot): **360**

### Step 2: Total students in Bachata or Bolero, but not FoxTrot.
Add the numbers from Step 1:
\[
297 \, \text{(Bachata only)} + 330 \, \text{(Bolero only)} + 360 \, \text{(Bachata and Bolero only)} = 987
\]

### Step 3: Total number of students.
To calculate the total number of students, sum up all the regions in the Venn diagram:
\[
297 + 360 + 330 + 272 + 322 + 289 + 312 + 352 = 2534
\]

### Step 4: Probability calculation.
The probability that a student competed in **Bachata or Bolero, but not FoxTrot** is the ratio of the relevant students to the total number of students:
\[
P = \frac{987}{2534} \approx 0.389
\]

Thus, the probability is approximately **0.389**.

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Do you have any questions or want more details? Here are some related questions you might find useful:

1. What is the probability that a student competed in all three events (Bachata, Bolero, and FoxTrot)?
2. What is the probability that a student competed in exactly two events?
3. What is the probability that a student competed in only FoxTrot?
4. What is the probability that a student did not compete in Bolero?
5. What is the probability that a student competed in Bachata and Bolero?

**Tip**: Always ensure that you're counting disjoint regions correctly in a Venn diagram to avoid double-counting overlapping sections.

If a student is chosen at random, what is the probability that the student competed in Bachata or Bolero, but not FoxTrot?

Calculate the probability that a randomly selected student competed in Bachata or Bolero, but not FoxTrot. This problem involves understanding set theory, Venn diagrams, and probability calculations, suitable for high school students.

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