Question 30·Hard·Probability and Conditional Probability
The table shows the distribution of employees at a technology firm by department and primary work arrangement.
| Department | Remote | Hybrid | In office |
|---|---|---|---|
| Engineering | 36 | 18 | 12 |
| Marketing | 20 | 16 | 10 |
| Finance | 8 | 12 | 30 |
| Human Resources | 6 | 8 | 18 |
To the nearest tenth of a percent, what percent of in-office employees work in the Finance department?
For table-and-percentage questions, always start by identifying what group the question is using as the total: the phrase "percent of ___" tells you what goes in the denominator. Then, from the table, find the specific subgroup named in the question (that goes in the numerator). Form the fraction (part ÷ whole), use your calculator to convert it to a decimal and then to a percent, and finally apply any requested rounding before matching to an answer choice. Staying disciplined about choosing the correct denominator prevents most mistakes on these problems.
Hints
Figure out what the denominator should be
When a question says "What percent of ___", the blank tells you what the total group (denominator) is. Ask yourself: is the total group all employees, all Finance employees, or all in-office employees?
Use the table to find the total in-office employees
Look only at the "In office" column and add the numbers from all departments to find how many employees work in the office overall.
Set up a part-over-whole fraction
Once you know the total number of in-office employees, use the number of Finance in-office employees as the numerator and the total in-office employees as the denominator, then convert that fraction to a percent.
Desmos Guide
Compute the percent in Desmos
In Desmos, type (30/70)*100 to represent (Finance in-office) ÷ (total in-office) × 100. Use the numerical output as the percent of in-office employees who work in Finance, and round that value to the nearest tenth to match an answer choice.
Step-by-step Explanation
Identify the total (the "whole") group
The phrase "percent of in-office employees" means the total group you care about is all in-office employees, across every department.
From the "In office" column:
- Engineering: 12
- Marketing: 10
- Finance: 30
- Human Resources: 18
Add these to find the total number of in-office employees:
So there are 70 in-office employees in total.
Identify the part of that group
Now find how many of those in-office employees are in the Finance department.
From the Finance row and "In office" column, there are 30 Finance employees who work in the office.
So the part is 30 (Finance, in office) and the whole is 70 (all in-office employees).
Form the fraction and convert to a percent
To find the desired percent, divide the part by the whole and then multiply by 100:
Now convert this decimal to a percent:
Rounded to the nearest tenth of a percent, this is , which matches answer choice C) 42.9%.