The cue for conditional probability is that a student is selected from a named group, not necessarily from everyone surveyed. To count a group described with “or,” add the two activity counts and subtract the students in both, who were counted twice. Use that group as the denominator and the students who meet the target as the numerator. Using the full survey total ignores the restriction.
Hints
- Hint 1
The word from limits who can be picked. The sample space, meaning all possible students in the selection, includes anyone in theater, volunteering, or both. Why isn’t the survey total automatically the denominator?
- Hint 2
The overlap is the group counted in both activities. Adding the activity totals counts those students twice. How can you correct the total before finding the probability?
- Hint 3
For a conditional probability, divide the target count inside the allowed group by the allowed group’s total. Every theater student belongs to the “theater or volunteer” group, including students who do both.
Step-by-step
Count the eligible group, then find the probability
Step 1Count each eligible student once
The selection includes students in theater or volunteering. Add the two activity counts, but the students in both were counted twice. Subtract the overlap once when counting an “or” group. The eligible count is .
- Step 2
Find the eligible total
Type in Desmos. It shows , so the denominator, the number of students who could be selected, is 36 rather than 60.
- Step 3
Count the theater students in that group
The target is theater participation, not just both activities. All theater students are eligible, including those who also volunteer. So the numerator, the count that meets the target, is , not .
- Step 4
Find the probability
Type in Desmos. It shows ; tap the fraction button to see . So the probability that the selected student participates in theater is . Choice A.