A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. The results of the survey are summarized in the following table. Preferred Fitness Area Spinning Room Climbing Wall Ellipticals Year 1-2 37 81 20 Class Level Year 3-4 71 86 47 Graduate Student 81 55 22 What is the probability that a randomly selected student is interested in a spinning room given that they are a graduate student?

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### Multiple Choice

Please select the correct answer from the options below:

1. ○ 0.513
2. ○ 0.381
3. ○ 0.684
4. ○ 0.129

Each option is marked with a circular radio button, allowing for only one selection. Please consider your answer carefully before making a choice.
Transcribed Image Text:### Multiple Choice Please select the correct answer from the options below: 1. ○ 0.513 2. ○ 0.381 3. ○ 0.684 4. ○ 0.129 Each option is marked with a circular radio button, allowing for only one selection. Please consider your answer carefully before making a choice.
### University Fitness Area Survey Results

A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. The survey results are summarized in the table below:

| **Class Level**       | **Preferred Fitness Area** |                         |                          |
|-----------------------|--------------------------- |-------------------------|------------------------- |
|                       | **Spinning Room**          | **Climbing Wall**       | **Ellipticals**          |
| **Year 1-2**          | 37                         | 81                      | 20                       |
| **Year 3-4**          | 71                         | 86                      | 47                       |
| **Graduate Student**  | 81                         | 55                      | 22                       |

### Probability Calculation

**Question:** What is the probability that a randomly selected student is interested in a spinning room given that they are a graduate student?

To find this probability, use the conditional probability formula:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Where:
- \( A \) is the event that a student is interested in a spinning room.
- \( B \) is the event that a student is a graduate student.
- \( P(A \cap B) \) is the joint probability that the student is a graduate student and is interested in a spinning room.
- \( P(B) \) is the probability that the student is a graduate student.

From the table:
- There are 81 graduate students interested in the spinning room.
- The total number of graduate students surveyed is \( 81 + 55 + 22 = 158 \).

Thus, the probability \( P(A|B) \) is:

\[ P(A|B) = \frac{81}{158} \]

This gives the probability that a randomly selected graduate student is interested in the spinning room.
Transcribed Image Text:### University Fitness Area Survey Results A university recently surveyed 500 students to determine which new fitness area to offer in its recreation facility. The survey results are summarized in the table below: | **Class Level** | **Preferred Fitness Area** | | | |-----------------------|--------------------------- |-------------------------|------------------------- | | | **Spinning Room** | **Climbing Wall** | **Ellipticals** | | **Year 1-2** | 37 | 81 | 20 | | **Year 3-4** | 71 | 86 | 47 | | **Graduate Student** | 81 | 55 | 22 | ### Probability Calculation **Question:** What is the probability that a randomly selected student is interested in a spinning room given that they are a graduate student? To find this probability, use the conditional probability formula: \[ P(A|B) = \frac{P(A \cap B)}{P(B)} \] Where: - \( A \) is the event that a student is interested in a spinning room. - \( B \) is the event that a student is a graduate student. - \( P(A \cap B) \) is the joint probability that the student is a graduate student and is interested in a spinning room. - \( P(B) \) is the probability that the student is a graduate student. From the table: - There are 81 graduate students interested in the spinning room. - The total number of graduate students surveyed is \( 81 + 55 + 22 = 158 \). Thus, the probability \( P(A|B) \) is: \[ P(A|B) = \frac{81}{158} \] This gives the probability that a randomly selected graduate student is interested in the spinning room.
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