The phrase “selected from” signals conditional probability: the selection is limited to a smaller group. Add the table rows for students who could be picked to get the denominator, then count those who meet the target for the numerator. The trap is using all students as the denominator or forgetting that students in “both” belong to each club.
Hints
- Hint 1
A condition limits who can be selected. Here, neither club means a student cannot be picked. Which three table rows remain?
- Hint 2
The numerator counts students in the eligible group who participate in chess. Include both-club students along with chess-only students.
Step-by-step
Restrict the group, then count chess players
Step 1Exclude students who cannot be picked
A condition limits the group a selection comes from. The student is selected from those in at least one club, so the 15 students in neither club cannot be picked. Count only students who could be selected in the denominator.
- Step 2
Find the eligible total
The eligible students are in three separate rows: chess only, art only, and both. Type in Desmos. It shows , the total number who could be selected.
- Step 3
Count the eligible chess players
Chess players include the 12 in chess only and the 5 in both clubs. Type ; Desmos shows . Counting only the chess-only row would leave out students who play chess and also do art.
- Step 4
Find the probability
A probability is the number who meet the target divided by the number who could be picked. Type ; Desmos shows , and its fraction button gives . So the probability that the selected student participates in chess is . Choice C.