A test was given to a group of students. The grades and gender are summarized below A Male 16 19 14 Female 20 11 2 Total 36 30 16 B C 89 Total 49 33 82 If one student is chosen at random from those who took the test, Find the probability that the student was male GIVEN they got a 'C'.

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## Test Scores by Gender

A test was given to a group of students. The grades and gender are summarized below:

|       | A  | B  | C  | Total |
|-------|----|----|----|-------|
| Male  | 16 | 19 | 14 | 49    |
| Female| 20 | 11 |  2 | 33    |
| Total | 36 | 30 | 16 | 82    |

- **Explanation:** This table outlines the distribution of grades (A, B, C) among male and female students, along with the total number of students for each category.

### Probability Problem

If one student is chosen at random from those who took the test, find the probability that the student was male **given** they got a 'C'.

To solve this, you need to compare the number of males who got a 'C' with the total number of students who received a 'C'. The conditional probability is calculated as follows: 

\[ P(\text{Male | C}) = \frac{\text{Number of males who got a 'C'}}{\text{Total number of students who got a 'C'}} \]

Given data: 
- Number of males who got a 'C' = 14
- Total number of students who got a 'C' = 16

Thus, the probability is \(\frac{14}{16} = \frac{7}{8}\).
Transcribed Image Text:## Test Scores by Gender A test was given to a group of students. The grades and gender are summarized below: | | A | B | C | Total | |-------|----|----|----|-------| | Male | 16 | 19 | 14 | 49 | | Female| 20 | 11 | 2 | 33 | | Total | 36 | 30 | 16 | 82 | - **Explanation:** This table outlines the distribution of grades (A, B, C) among male and female students, along with the total number of students for each category. ### Probability Problem If one student is chosen at random from those who took the test, find the probability that the student was male **given** they got a 'C'. To solve this, you need to compare the number of males who got a 'C' with the total number of students who received a 'C'. The conditional probability is calculated as follows: \[ P(\text{Male | C}) = \frac{\text{Number of males who got a 'C'}}{\text{Total number of students who got a 'C'}} \] Given data: - Number of males who got a 'C' = 14 - Total number of students who got a 'C' = 16 Thus, the probability is \(\frac{14}{16} = \frac{7}{8}\).
Expert Solution
Step 1
  A B C total
male 16 19 14 49
female 20 11 2 23
total 36 30 16 80
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