The phrase who volunteers signals conditional probability: you already know which group the selected student belongs to. In a two-way table, use that group’s row or column total as the denominator, then find the matching cell for the numerator. Restrict the group first, then count within it. Dividing by the survey’s grand total ignores the condition.
Hints
- Hint 1
A condition is something already known about the selected student. Who volunteers limits the possible students to one row. What total appears at the end of that row?
- Hint 2
A favorable outcome is a pick that matches what the question asks for. Stay in the volunteer row and look under the instrument column. How many volunteers play?
- Hint 3
A conditional probability counts matches inside the group already fixed. Put the volunteers who play over all volunteers, not over all students in the survey.
Step-by-step
Use the volunteer row
Step 1Choose the group being selected from
No Desmos needed. The table gives both counts, and the fraction simplifies by hand. The words who volunteers tell you the selected student is a volunteer. So only the Volunteers row is possible, and its total, , is the denominator. Using all students would ignore that condition.
- Step 2
Find the volunteers who play
Read across the Volunteers row to the Plays a musical instrument column. The cell where they meet contains , so volunteers match what the question asks for.
- Step 3
Write the probability
Probability is the matching count over the count that could be selected. Here, both counts come from the volunteer row:
The vertical bar means “given that.”
- Step 4
Simplify the fraction
Both and are divisible by . Divide the top and bottom by :
That’s the probability that a selected volunteer plays a musical instrument. Choice C.