To tackle the problem of finding probabilities related to the accountants in the personnel department, we can break down the information provided into manageable parts. We have a total of 200 accountants categorized by age and degree type. Let’s analyze the data step by step to find the required probabilities.
Understanding the Data
The data can be summarized in a table format for clarity:
| Age Group |
Bachelor’s Degree Only |
Master’s Degree |
| Under 30 |
90 |
10 |
| 30 to 40 |
20 |
30 |
| Over 40 |
40 |
10 |
Now, let’s calculate the total number of accountants with each type of degree:
- Total with Bachelor’s Degree: 90 + 20 + 40 = 150
- Total with Master’s Degree: 10 + 30 + 10 = 50
Calculating Probabilities
a) Probability of Having Only a Bachelor’s Degree
The probability of selecting an accountant with only a bachelor’s degree can be calculated using the formula:
Probability (P) = (Number of accountants with a bachelor’s degree) / (Total number of accountants)
Substituting the values:
P(Bachelor’s Degree) = 150 / 200 = 0.75
Thus, the probability that a randomly selected accountant has only a bachelor’s degree is 0.75 or 75%.
b) Probability of Having a Master’s Degree Given They Are Over 40
To find this conditional probability, we use the formula:
P(Master’s | Over 40) = (Number of accountants over 40 with a master’s degree) / (Total number of accountants over 40)
From the data, we know:
- Number of accountants over 40 with a master’s degree = 10
- Total number of accountants over 40 = 40 (Bachelor’s) + 10 (Master’s) = 50
Now substituting these values:
P(Master’s | Over 40) = 10 / 50 = 0.2
Therefore, the probability that an accountant is over 40 and has a master’s degree is 0.2 or 20%.
c) Probability of Being Under 30 Given They Have a Bachelor’s Degree
For this conditional probability, we apply the formula:
P(Under 30 | Bachelor’s) = (Number of accountants under 30 with a bachelor’s degree) / (Total number of accountants with a bachelor’s degree)
From our earlier calculations:
- Number of accountants under 30 with a bachelor’s degree = 90
- Total number of accountants with a bachelor’s degree = 150
Substituting these values gives us:
P(Under 30 | Bachelor’s) = 90 / 150 = 0.6
Thus, the probability that an accountant is under 30 given they have a bachelor’s degree is 0.6 or 60%.
Summary of Results
- Probability of having only a bachelor’s degree: 0.75 (75%)
- Probability of having a master’s degree given they are over 40: 0.2 (20%)
- Probability of being under 30 given they have a bachelor’s degree: 0.6 (60%)
By breaking down the problem and applying the principles of probability, we can effectively analyze the data and draw meaningful conclusions about the accountants in the company.
