Question 8·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis
The table shows the distribution of 160 interns and their departments at a company. Each intern is categorized in exactly one department.
| Department | Frequency |
|---|---|
| Biology | 40 |
| Chemistry | 32 |
| Physics | 24 |
| Engineering or Computer Science | 64 |
If one of the 160 interns is selected at random, the probability of selecting an intern who is categorized as Engineering, given that the intern is not categorized as Biology and not categorized as Physics, is . How many of these interns are categorized as Computer Science?
For conditional probability problems with tables, first translate the condition (the “given” part) into a smaller sample space by excluding the listed categories. Then write the conditional probability as a fraction: (count of the target category within that sample space) divided by (total count in that sample space). Solve for the target count, and only then use any combined-category totals to find the requested subcategory by subtraction.
Hints
Rewrite the condition
Under the condition “not Biology and not Physics,” which departments are still possible based on the table?
Set up the conditional probability as a fraction
Use
Here, is “not Biology and not Physics.”
Use the combined category at the end
Once you find how many are Engineering, remember that Engineering is part of the “Engineering or Computer Science” total of 64.
Desmos Guide
Compute the conditional sample space size
Enter the expression 32+64 to confirm the number of interns who are not in Biology and not in Physics.
Compute the number in Engineering from the conditional probability
Enter 96*(7/24) to compute how many interns are categorized as Engineering under that condition.
Subtract from the combined total
Enter 64-28 (or 64-(96*(7/24))) to get the number categorized as Computer Science.
Step-by-step Explanation
Find the conditional sample space
“Not categorized as Biology and not categorized as Physics” means the intern must be in Chemistry or in Engineering or Computer Science.
So the number of interns in this sample space is
Use the conditional probability to find the number in Engineering
The conditional probability is
So
Compute Engineering
So 28 interns are categorized as Engineering.
Subtract from the combined category to get Computer Science
Engineering and Computer Science together total 64 interns. Therefore,
The correct answer is 36.