ory 31 A test was given to a group of students. The grades and gender are summarized below A B C Total Male 10 15 9 34 Female 12 14 3 29 Total 22 29 12 63 If one student is chosen at random from those who took the test, Find the probability that the student was female GIVEN they got a 'C'. Round answer 4 places after the decimal if needed. Submit Question 86°F Sunny SM DALL 10:24 6/21/20
ory 31 A test was given to a group of students. The grades and gender are summarized below A B C Total Male 10 15 9 34 Female 12 14 3 29 Total 22 29 12 63 If one student is chosen at random from those who took the test, Find the probability that the student was female GIVEN they got a 'C'. Round answer 4 places after the decimal if needed. Submit Question 86°F Sunny SM DALL 10:24 6/21/20
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![### Probability and Statistics: Analyzing Gender and Grades
In this lesson, we will analyze the probability of an event occurring based on given data. Let's consider the following scenario:
#### Test Data Summary
A test was administered to a group of students. The table below summarizes the grades (A, B, C) received by male and female students:
| Grade/Gender | A | B | C | Total |
|--------------|----|----|----|-------|
| Male | 10 | 15 | 9 | 34 |
| Female | 12 | 14 | 3 | 29 |
| Total | 22 | 29 | 12 | 63 |
#### Question:
If one student is chosen at random from those who took the test, find the probability that the student was female GIVEN they got a ‘C’. Round the answer to 4 decimal places if needed.
### Step-by-Step Solution:
1. **Identify the Given Data:**
- Total number of students who got a ‘C’: 12.
- Number of female students who got a ‘C’: 3.
2. **Conditional Probability Formula:**
The conditional probability that a student is female given they got a ‘C’ is given by:
\[
P(\text{Female} \mid \text{C}) = \frac{P(\text{Female and C})}{P(\text{C})}
\]
3. **Calculate the Probabilities:**
- \(P(\text{Female and C})\): This is the number of female students who got a ‘C’ divided by the total number of students.
\[
P(\text{Female and C}) = \frac{3}{63}
\]
- \(P(\text{C})\): This is the total number of students who got a ‘C’ divided by the total number of students.
\[
P(\text{C}) = \frac{12}{63}
\]
4. **Compute the Conditional Probability:**
\[
P(\text{Female} \mid \text{C}) = \frac{\frac{3}{63}}{\frac{12}{63}} = \frac{3}{12} = \frac{1}{4} = 0.25
\]
Thus, the probability that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4299bab-cfe6-4df1-82fa-bdefd18a2ba9%2F124fbdcd-71b0-42f7-8abd-1e5776528af9%2Falblylj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics: Analyzing Gender and Grades
In this lesson, we will analyze the probability of an event occurring based on given data. Let's consider the following scenario:
#### Test Data Summary
A test was administered to a group of students. The table below summarizes the grades (A, B, C) received by male and female students:
| Grade/Gender | A | B | C | Total |
|--------------|----|----|----|-------|
| Male | 10 | 15 | 9 | 34 |
| Female | 12 | 14 | 3 | 29 |
| Total | 22 | 29 | 12 | 63 |
#### Question:
If one student is chosen at random from those who took the test, find the probability that the student was female GIVEN they got a ‘C’. Round the answer to 4 decimal places if needed.
### Step-by-Step Solution:
1. **Identify the Given Data:**
- Total number of students who got a ‘C’: 12.
- Number of female students who got a ‘C’: 3.
2. **Conditional Probability Formula:**
The conditional probability that a student is female given they got a ‘C’ is given by:
\[
P(\text{Female} \mid \text{C}) = \frac{P(\text{Female and C})}{P(\text{C})}
\]
3. **Calculate the Probabilities:**
- \(P(\text{Female and C})\): This is the number of female students who got a ‘C’ divided by the total number of students.
\[
P(\text{Female and C}) = \frac{3}{63}
\]
- \(P(\text{C})\): This is the total number of students who got a ‘C’ divided by the total number of students.
\[
P(\text{C}) = \frac{12}{63}
\]
4. **Compute the Conditional Probability:**
\[
P(\text{Female} \mid \text{C}) = \frac{\frac{3}{63}}{\frac{12}{63}} = \frac{3}{12} = \frac{1}{4} = 0.25
\]
Thus, the probability that
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