Giving a test to a group of students, the grades and gender are summarized below Grades and Gender B с Male Female Total Calculator A 20 2 22 13 14 27 5 8 13 Total 38 24 62 If one student is chosen at random, find the probability that the student was female OR got an "B". Round your answer to 4 decimal places.
Giving a test to a group of students, the grades and gender are summarized below Grades and Gender B с Male Female Total Calculator A 20 2 22 13 14 27 5 8 13 Total 38 24 62 If one student is chosen at random, find the probability that the student was female OR got an "B". Round your answer to 4 decimal places.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![**Probability of Event: Female or Grade "B"**
On an educational website, we present the following dataset about a group of students categorized by grades and gender. The distribution of grades is given in the table below:
| | A | B | C | **Total** |
|-------|----|----|----|--------|
| **Male** | 20 | 13 | 5 | 38 |
| **Female** | 2 | 14 | 8 | 24 |
| **Total** | 22 | 27 | 13 | 62 |
**Objective:**
Determine the probability that a student chosen at random is either female or received a grade of "B".
**Calculation:**
- Total number of students: 62
- Total females: 24
- Total students with grade "B": 27
- Female students with grade "B": 14 (already counted in both categories)
Using the formula for the probability of the union of two events \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \):
\[ P(\text{Female or "B"}) = P(\text{Female}) + P(\text{"B"}) - P(\text{Female and "B"}) \]
Where:
- \( P(\text{Female}) = \frac{24}{62} \)
- \( P(\text{"B"}) = \frac{27}{62} \)
- \( P(\text{Female and "B"}) = \frac{14}{62} \)
Substitute the values:
\[ P(\text{Female or "B"}) = \frac{24}{62} + \frac{27}{62} - \frac{14}{62} = \frac{37}{62} \]
\- Probability (rounded to four decimal places): 0.5968
**Conclusion:**
The probability that a randomly selected student is either female or received a "B" grade is approximately 0.5968.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8650f35a-2b12-4856-b432-6b1adb33d792%2F87324b14-a078-4a2a-870a-0ca9c5a561b8%2F8aqq1p_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability of Event: Female or Grade "B"**
On an educational website, we present the following dataset about a group of students categorized by grades and gender. The distribution of grades is given in the table below:
| | A | B | C | **Total** |
|-------|----|----|----|--------|
| **Male** | 20 | 13 | 5 | 38 |
| **Female** | 2 | 14 | 8 | 24 |
| **Total** | 22 | 27 | 13 | 62 |
**Objective:**
Determine the probability that a student chosen at random is either female or received a grade of "B".
**Calculation:**
- Total number of students: 62
- Total females: 24
- Total students with grade "B": 27
- Female students with grade "B": 14 (already counted in both categories)
Using the formula for the probability of the union of two events \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \):
\[ P(\text{Female or "B"}) = P(\text{Female}) + P(\text{"B"}) - P(\text{Female and "B"}) \]
Where:
- \( P(\text{Female}) = \frac{24}{62} \)
- \( P(\text{"B"}) = \frac{27}{62} \)
- \( P(\text{Female and "B"}) = \frac{14}{62} \)
Substitute the values:
\[ P(\text{Female or "B"}) = \frac{24}{62} + \frac{27}{62} - \frac{14}{62} = \frac{37}{62} \]
\- Probability (rounded to four decimal places): 0.5968
**Conclusion:**
The probability that a randomly selected student is either female or received a "B" grade is approximately 0.5968.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON