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Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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![The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is:
- ○ 0.0667
- ○ 0.567
- ○ 0.667
- ○ 0.833
**Explanation:**
To determine the probability that an employee is married and has a college degree, we first need the number of married employees with college degrees.
1. **Total Employees with College Degrees**: 400
2. **Single College Graduates**: 60
Therefore, the number of married employees with college degrees is 400 - 60 = 340.
**Probability Calculation:**
The probability is the ratio of married employees with college degrees to the total number of employees.
\[ \text{Probability} = \frac{340}{600} = 0.567 \]
Thus, the correct option is:
- ○ 0.567](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcdd8481c-6635-4f27-b260-3ac85dff9d75%2Fbdee6163-d6a3-4bfd-9c9d-1c971c325b42%2Fl2vav88_processed.png&w=3840&q=75)
Transcribed Image Text:The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is:
- ○ 0.0667
- ○ 0.567
- ○ 0.667
- ○ 0.833
**Explanation:**
To determine the probability that an employee is married and has a college degree, we first need the number of married employees with college degrees.
1. **Total Employees with College Degrees**: 400
2. **Single College Graduates**: 60
Therefore, the number of married employees with college degrees is 400 - 60 = 340.
**Probability Calculation:**
The probability is the ratio of married employees with college degrees to the total number of employees.
\[ \text{Probability} = \frac{340}{600} = 0.567 \]
Thus, the correct option is:
- ○ 0.567
Expert Solution
Step 1
probability is the chance of occurrence of an event. It lies between 0 to 1.
According to the given sum, We will construct a contingency table for the ease of understanding.
| Single | Married | Total | |
| college | 60 | 340 | 400 |
| No college | 40 | 160 | 200 |
| total | 100 | 500 | 600 |
We have represented the given data in the above table and filled in the necessary information.
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