Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 3 8 14 25 Female 19 20 6 45 Total 22 28 20 70 If one student is chosen at random, Find the probability that the student was female AND got a "B". Round answer 4 places after the decimal if needed. 0.7571 X
Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 3 8 14 25 Female 19 20 6 45 Total 22 28 20 70 If one student is chosen at random, Find the probability that the student was female AND got a "B". Round answer 4 places after the decimal if needed. 0.7571 X
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![### Probability and Statistics: Gender and Grade Distribution
#### Given Data:
A study was conducted where a group of students was administered a test, and the summary of their grades and gender is tabulated below:
| | A | B | C | Total |
|--------|-----|-----|-----|-------|
| Male | 3 | 8 | 14 | 25 |
| Female | 19 | 20 | 6 | 45 |
| **Total** | **22** | **28** | **20** | **70** |
#### Problem:
If one student is chosen at random from this group, find the probability that the student selected is a female and received a "B" grade.
#### Solution:
Total number of students = 70
Number of females who received a "B" grade = 20
The probability of selecting a female student who got a "B" grade is calculated as follows:
\[
\text{Probability (Female and B)} = \frac{\text{Number of females who got B}}{\text{Total number of students}} = \frac{20}{70} = 0.2857
\]
**Conclusion:**
The probability that a randomly selected student from this group is a female who received a "B" grade is 0.2857 (rounded to four decimal places).
#### Interactive Component:
Please verify your understanding by submitting your answer:
```
Enter your answer: 0.2857
Submit Question
```
#### Additional Notes:
- Ensure all probability answers are rounded to four decimal places if required.
- Review the table and counts carefully for accurate calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4299bab-cfe6-4df1-82fa-bdefd18a2ba9%2F0421a10c-8720-4a06-becd-ad188465685c%2Fj0zbfq9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability and Statistics: Gender and Grade Distribution
#### Given Data:
A study was conducted where a group of students was administered a test, and the summary of their grades and gender is tabulated below:
| | A | B | C | Total |
|--------|-----|-----|-----|-------|
| Male | 3 | 8 | 14 | 25 |
| Female | 19 | 20 | 6 | 45 |
| **Total** | **22** | **28** | **20** | **70** |
#### Problem:
If one student is chosen at random from this group, find the probability that the student selected is a female and received a "B" grade.
#### Solution:
Total number of students = 70
Number of females who received a "B" grade = 20
The probability of selecting a female student who got a "B" grade is calculated as follows:
\[
\text{Probability (Female and B)} = \frac{\text{Number of females who got B}}{\text{Total number of students}} = \frac{20}{70} = 0.2857
\]
**Conclusion:**
The probability that a randomly selected student from this group is a female who received a "B" grade is 0.2857 (rounded to four decimal places).
#### Interactive Component:
Please verify your understanding by submitting your answer:
```
Enter your answer: 0.2857
Submit Question
```
#### Additional Notes:
- Ensure all probability answers are rounded to four decimal places if required.
- Review the table and counts carefully for accurate calculations.
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