Question 17·Medium·Probability and Conditional Probability
| Human Resources | Accounting | |
|---|---|---|
| Bachelor’s degree | 4 | 3 |
| Master’s degree | 2 | 6 |
The table above shows the number of people who work in the Human Resources and Accounting departments of a company and the highest level of education they have completed. A person from one of these departments is to be chosen at random. If the person chosen works in the Human Resources department, what is the probability that the highest level of education the person completed is a master’s degree?
For table-based conditional probability questions, first carefully identify the condition (for example, “if the person chosen works in Human Resources”) and use it to restrict your sample space to one row or column. Then, within that restricted group, compute the probability as (number with the desired characteristic) ÷ (total in that restricted group). Avoid common traps like using the total from the whole table or swapping the condition and the event.
Hints
Identify the restricted group
Focus only on the people in the Human Resources department. How many people are in that department in total?
Count the favorable outcomes
Within the Human Resources group, how many people have a master’s degree?
Form the probability as a fraction
Probability is (number in the desired category) divided by (total number in the group you are considering). Use your counts from the first two hints to form this fraction, then simplify it.
Desmos Guide
Compute the conditional probability
In Desmos’s expression line, type 2/(4+2) to represent “number of master’s in HR divided by total HR employees.” The numerical value that Desmos shows for this fraction is the probability you want.
Step-by-step Explanation
Understand what “if the person chosen works in Human Resources” means
The phrase “If the person chosen works in the Human Resources department” tells you that you are only considering people in the Human Resources department. This is a conditional probability: you restrict your group to the Human Resources employees before finding the probability.
Find the total number of Human Resources employees
Look at the Human Resources column in the table:
- Bachelor’s degree: 4 people
- Master’s degree: 2 people
So the total number of Human Resources employees is .
Find how many of those have master’s degrees
Still staying in the Human Resources column, count only those with master’s degrees. The table shows 2 Human Resources employees with a master’s degree.
Write and simplify the probability
The probability that a randomly chosen Human Resources employee has a master’s degree is
Now simplify by dividing numerator and denominator by 2:
So the correct answer is , which corresponds to choice B.