The phrase “selected from” signals conditional probability: the pick is limited to a particular group. Use that group’s size as the denominator, then count how many people within that group have the requested trait. Using the survey-wide total instead answers a different question about all students.
Hints
- Hint 1
A sample space is everyone who could be picked. The phrase “selected from” narrows that set. Which students are still possible picks here?
- Hint 2
For a conditional probability, count the people with the requested trait inside the selected group. What count goes on top, and what group total goes underneath?
Step-by-step
Restrict the group, then divide
Step 1Choose the group that can be picked
The student is selected from those who bring lunch from home. Those students are the sample space, meaning everyone who could be picked. The denominator is the size of that group, not all students surveyed.
- Step 2
Count instrument players within that group
Of those students, play an instrument. Put the count you want over the count that could be picked:
The bar means “given that” the student brings lunch from home.
- Step 3
Simplify the probability
Type in Desmos. It shows ; tap the fraction button to see . So the probability that a student picked from the home-lunch group plays an instrument is . Choice A.