A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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**Probability of Selecting a Male Student or a Student with an "A" Grade**

In this probability exercise, we analyze a group of students based on their grades and gender. The following table summarizes the distribution:

|        | A  | B  | C  | Total |
|--------|----|----|----|-------|
| Male   | 13 | 8  | 14 | 35    |
| Female | 19 | 4  | 5  | 28    |
| Total  | 32 | 12 | 19 | 63    |

**Objective:**
Determine the probability that a randomly selected student is either male or has received an "A" grade.

To solve this, we need to calculate:
1. Total students who are male.
2. Total students who received an "A".
3. Use the formula for probability with "or" condition:
   \[
   P(\text{Male or A}) = P(\text{Male}) + P(\text{A}) - P(\text{Male and A})
   \]

- **Total students**: 63
- **Total males**: 35
- **Total students with an "A"**: 32
- **Males with an "A"**: 13

Using the formula:
\[
P(\text{Male or A}) = \frac{35}{63} + \frac{32}{63} - \frac{13}{63} = \frac{54}{63} = \frac{18}{21} \approx 0.857
\]

**Conclusion:**
The probability that a randomly selected student is either male or received an "A" is approximately 0.857, or 85.7%.
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Transcribed Image Text:**Probability of Selecting a Male Student or a Student with an "A" Grade** In this probability exercise, we analyze a group of students based on their grades and gender. The following table summarizes the distribution: | | A | B | C | Total | |--------|----|----|----|-------| | Male | 13 | 8 | 14 | 35 | | Female | 19 | 4 | 5 | 28 | | Total | 32 | 12 | 19 | 63 | **Objective:** Determine the probability that a randomly selected student is either male or has received an "A" grade. To solve this, we need to calculate: 1. Total students who are male. 2. Total students who received an "A". 3. Use the formula for probability with "or" condition: \[ P(\text{Male or A}) = P(\text{Male}) + P(\text{A}) - P(\text{Male and A}) \] - **Total students**: 63 - **Total males**: 35 - **Total students with an "A"**: 32 - **Males with an "A"**: 13 Using the formula: \[ P(\text{Male or A}) = \frac{35}{63} + \frac{32}{63} - \frac{13}{63} = \frac{54}{63} = \frac{18}{21} \approx 0.857 \] **Conclusion:** The probability that a randomly selected student is either male or received an "A" is approximately 0.857, or 85.7%.
Expert Solution
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Step 1

Given information-

We have given the grades and gender of a group of students.

Probability homework question answer, step 1, image 1

We have to find the probability that the student was male OR got an "A".

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