Giving a test to a group of students, the grades and gender are summarized below Grades vs. Gender ABC Male 6 2 18 Female 8 19 11 If one student was chosen at random, find the probability that the student got a B. Probability = (Round to 4 decimal places)
Giving a test to a group of students, the grades and gender are summarized below Grades vs. Gender ABC Male 6 2 18 Female 8 19 11 If one student was chosen at random, find the probability that the student got a B. Probability = (Round to 4 decimal places)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Probability of a Student Getting a B**
In a study conducted where a test was administered to a group of students, the distribution of grades relative to gender is summarized in the table below:
| | A | B | C |
|--------|---|----|----|
| Male | 6 | 2 | 18 |
| Female | 8 | 19 | 11 |
*Table 1: Distribution of Grades vs. Gender*
**Problem:**
If one student was chosen at random, determine the probability that the student received a grade of B.
**Solution:**
1. **Calculate the Total Number of Students:**
Total Students = (Males with A + Males with B + Males with C) + (Females with A + Females with B + Females with C)
\[
\text{Total Students} = (6 + 2 + 18) + (8 + 19 + 11) = 44
\]
2. **Calculate the Total Number of Students Who Got a B:**
Total Students with B = Males with B + Females with B
\[
\text{Total Students with B} = 2 + 19 = 21
\]
3. **Calculate the Probability:**
\[
\text{Probability} = \frac{\text{Total Students with B}}{\text{Total Students}} = \frac{21}{44}
\]
4. **Round the Probability to 4 Decimal Places:**
\[
\text{Probability} = 0.4773
\]
Therefore, the probability that a randomly chosen student got a B is **0.4773**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11f84057-ddc6-4a16-833f-eeebb801b1ce%2F1cc78787-0ad3-4479-988f-711f9cece40b%2Fnn04a0e_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability of a Student Getting a B**
In a study conducted where a test was administered to a group of students, the distribution of grades relative to gender is summarized in the table below:
| | A | B | C |
|--------|---|----|----|
| Male | 6 | 2 | 18 |
| Female | 8 | 19 | 11 |
*Table 1: Distribution of Grades vs. Gender*
**Problem:**
If one student was chosen at random, determine the probability that the student received a grade of B.
**Solution:**
1. **Calculate the Total Number of Students:**
Total Students = (Males with A + Males with B + Males with C) + (Females with A + Females with B + Females with C)
\[
\text{Total Students} = (6 + 2 + 18) + (8 + 19 + 11) = 44
\]
2. **Calculate the Total Number of Students Who Got a B:**
Total Students with B = Males with B + Females with B
\[
\text{Total Students with B} = 2 + 19 = 21
\]
3. **Calculate the Probability:**
\[
\text{Probability} = \frac{\text{Total Students with B}}{\text{Total Students}} = \frac{21}{44}
\]
4. **Round the Probability to 4 Decimal Places:**
\[
\text{Probability} = 0.4773
\]
Therefore, the probability that a randomly chosen student got a B is **0.4773**.
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