https://file.aiquickdraw.com/mathbot/file/1726227734494q5d446ez.jpg

Let's analyze the problem step by step based on the table provided.

### Table Information:
- **Rows:** Attended or did not attend the study session.
- **Columns:** Passed midterm or did not pass midterm.

The table looks like this:

|                     | Passed midterm | Did not pass midterm |
|---------------------|----------------|----------------------|
| **Attended study session**   | 63             | 8                    |
| **Did not attend study session** | 12             | 17                   |

The total number of students who passed the midterm is the sum of the students who attended the study session and passed, and the students who did not attend but still passed:
\[ 63 \ (\text{attended}) + 12 \ (\text{did not attend}) = 75 \]

### Question:
You are asked to find the probability that a randomly selected student who **passed the midterm** did **not** attend the study session.

#### Total number of students who passed the midterm = 75

#### Number of students who passed the midterm and did not attend the study session = 12

### Probability Formula:
\[
P(\text{Did not attend | Passed}) = \frac{\text{Number of students who did not attend and passed}}{\text{Total number of students who passed}}
\]
\[
P(\text{Did not attend | Passed}) = \frac{12}{75} = \frac{4}{25}
\]

So, the probability that a student who passed the midterm did not attend the study session is \( \frac{4}{25} \) or 0.16 (16%).

Would you like further clarification or details on this? 

Here are 5 related questions to expand on this topic:
1. What is the probability that a student who attended the study session passed the midterm?
2. What is the probability that a student did not pass the midterm?
3. How would the probability change if only students who attended the session were considered?
4. What is the total number of students who did not attend the study session?
5. What is the probability of randomly selecting a student who did not attend the study session?

### Tip:
When dealing with conditional probabilities, always identify the subset (e.g., students who passed the midterm) before calculating the likelihood of a specific condition (e.g., did not attend).

If one of the students is chosen at random from those who passed the midterm, what is the probability that student did not attend the study session?

Find the probability that a student who passed the midterm did not attend the study session. Using a conditional probability formula, this problem explores student attendance and midterm performance. Based on data from a study of 100 students, we calculate that the probability is 16%. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation