Giving a test to a group of students, the grades and gender are summarized below A Total Male 14 16 20 50 Female 17 18 40 Total 31 34 25 90 If one student is chosen at random, Find the probability that the student was male OR got an "A".
Giving a test to a group of students, the grades and gender are summarized below A Total Male 14 16 20 50 Female 17 18 40 Total 31 34 25 90 If one student is chosen at random, Find the probability that the student was male OR got an "A".
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![**Transcript for Educational Website**
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**Question:**
Giving a test to a group of students, the grades and gender are summarized below:
| | A | B | C | Total |
|-------|----|----|----|-------|
| Male | 14 | 16 | 20 | 50 |
| Female| 17 | 18 | 5 | 40 |
| Total | 31 | 34 | 25 | 90 |
If one student is chosen at random, find the probability that the student was male OR got an "A".
**Explanation:**
The table above displays the distribution of grades (A, B, C) among male and female students. The total number of students is 90, with 50 males and 40 females.
To find the probability that a randomly chosen student is male OR received an "A":
1. Calculate the total number of males = 50.
2. Calculate the total number of students who received an "A" = 31.
3. Since there is an overlap (male students who received an "A"), subtract the double-counted students (male students with "A"), which is 14.
Apply the formula:
\[ P(\text{Male OR A}) = P(\text{Male}) + P(\text{A}) - P(\text{Male AND A}) \]
Therefore:
\[ P(\text{Male OR A}) = \frac{50}{90} + \frac{31}{90} - \frac{14}{90} \]
- Simplify:
\[ P(\text{Male OR A}) = \frac{50 + 31 - 14}{90} = \frac{67}{90} \]
Hence, the probability that the student chosen is male OR got an "A" is \(\frac{67}{90}\).
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Transcribed Image Text:**Transcript for Educational Website**
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**Question:**
Giving a test to a group of students, the grades and gender are summarized below:
| | A | B | C | Total |
|-------|----|----|----|-------|
| Male | 14 | 16 | 20 | 50 |
| Female| 17 | 18 | 5 | 40 |
| Total | 31 | 34 | 25 | 90 |
If one student is chosen at random, find the probability that the student was male OR got an "A".
**Explanation:**
The table above displays the distribution of grades (A, B, C) among male and female students. The total number of students is 90, with 50 males and 40 females.
To find the probability that a randomly chosen student is male OR received an "A":
1. Calculate the total number of males = 50.
2. Calculate the total number of students who received an "A" = 31.
3. Since there is an overlap (male students who received an "A"), subtract the double-counted students (male students with "A"), which is 14.
Apply the formula:
\[ P(\text{Male OR A}) = P(\text{Male}) + P(\text{A}) - P(\text{Male AND A}) \]
Therefore:
\[ P(\text{Male OR A}) = \frac{50}{90} + \frac{31}{90} - \frac{14}{90} \]
- Simplify:
\[ P(\text{Male OR A}) = \frac{50 + 31 - 14}{90} = \frac{67}{90} \]
Hence, the probability that the student chosen is male OR got an "A" is \(\frac{67}{90}\).
**Additional Help:**
- [Video](#)
- [Message Instructor](#)
- Use [Calculator](#)
Submit your answer using the button below.
**Submit Question**
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Expert Solution
Step 1
Given
Male=50
Female=40
Step by step
Solved in 2 steps with 1 images
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