Dana Hills High School was considering going back to campus rather than remote instruction for the remainder of the semester. To make this decision, the school sent out a survey to students, parents, teachers, and staff to see if they would prefer remote or on campus instruction. The results of the survey are given in the table below. Find the probability that a person prefers on-campus instruction or is a parent. Student Parent Teacher Staff ТОTAL Remote 54 78 59 36 227 On-Campus 79 82 37 55 253 No Preference 23 12 8 11 54 TOTAL 156 172 104 102 534 O 0.796 O 0.642 0.689 O 0.782 O 0.637

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### Dana Hills High School Instruction Preference Survey Results

**Scenario:**

Dana Hills High School was considering returning to campus-based instruction rather than continuing remote learning for the remainder of the semester. To aid in this decision, the school sent out a survey to students, parents, teachers, and staff to determine their preferences for either remote or on-campus instruction. The survey results are summarized in the table below.

**Results Table:**

|                | Student | Parent | Teacher | Staff | TOTAL |
|----------------|---------|--------|---------|-------|-------|
| **Remote**     | 54      | 78     | 59      | 36    | 227   |
| **On-Campus**  | 79      | 82     | 37      | 55    | 253   |
| **No Preference** | 23   | 12     | 8       | 11    | 54    |
| **TOTAL**      | 156     | 172    | 104     | 102   | 534   |

**Task:**

Find the probability that a person prefers on-campus instruction or is a parent.

**Options:**

- 0.796
- 0.642
- 0.689
- 0.782
- 0.637

**Explanation:**

1. **Calculating the Probability:**

To determine this probability, use the inclusion-exclusion principle. The formula for the probability \( P(A \cup B) \) where \( A \) is the event of a person preferring on-campus instruction, and \( B \) is the event of a person being a parent, is given by:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

2. **Define Events:**

   - \( A \): Prefers on-campus instruction
     - Total people who prefer on-campus instruction: 253
   - \( B \): Is a parent
     - Total parents: 172
   - \( A \cap B \): Parents who prefer on-campus instruction
     - Parents preferring on-campus instruction: 82

3. **Calculate Probabilities:**

   - \( P(A) = \frac{253}{534} \)
   - \( P(B) = \frac{172}{534} \)
   - \( P(A \cap B) = \frac{
Transcribed Image Text:### Dana Hills High School Instruction Preference Survey Results **Scenario:** Dana Hills High School was considering returning to campus-based instruction rather than continuing remote learning for the remainder of the semester. To aid in this decision, the school sent out a survey to students, parents, teachers, and staff to determine their preferences for either remote or on-campus instruction. The survey results are summarized in the table below. **Results Table:** | | Student | Parent | Teacher | Staff | TOTAL | |----------------|---------|--------|---------|-------|-------| | **Remote** | 54 | 78 | 59 | 36 | 227 | | **On-Campus** | 79 | 82 | 37 | 55 | 253 | | **No Preference** | 23 | 12 | 8 | 11 | 54 | | **TOTAL** | 156 | 172 | 104 | 102 | 534 | **Task:** Find the probability that a person prefers on-campus instruction or is a parent. **Options:** - 0.796 - 0.642 - 0.689 - 0.782 - 0.637 **Explanation:** 1. **Calculating the Probability:** To determine this probability, use the inclusion-exclusion principle. The formula for the probability \( P(A \cup B) \) where \( A \) is the event of a person preferring on-campus instruction, and \( B \) is the event of a person being a parent, is given by: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] 2. **Define Events:** - \( A \): Prefers on-campus instruction - Total people who prefer on-campus instruction: 253 - \( B \): Is a parent - Total parents: 172 - \( A \cap B \): Parents who prefer on-campus instruction - Parents preferring on-campus instruction: 82 3. **Calculate Probabilities:** - \( P(A) = \frac{253}{534} \) - \( P(B) = \frac{172}{534} \) - \( P(A \cap B) = \frac{
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