The phrase selected from among students in at least one club limits the sample space, the group that can be picked. Add the two club counts, then subtract the overlap once so each student is counted once. Put the number in the requested club over that total. Students in both clubs still count as members of the requested club.
Hints
- Hint 1
At least one includes students in either club and students in both. The sample space is everyone who could be picked. How can you combine the club counts without counting anyone twice?
- Hint 2
Adding the two club totals counts students in both twice. Subtract that shared count once, not twice: those students still belong in the group being sampled.
- Hint 3
A probability is the number who meet the target divided by the number who could be picked. Students in both clubs still participate in art. Should they stay in the art count?
Step-by-step
Count the eligible students once
Step 1Build the count of students who could be picked
The student is picked from those in at least one club. Adding art students and coding students counts each of the students in both clubs twice. Subtract once so each eligible student is counted once:
- Step 2
Find the total eligible group
Type in Desmos. It shows , so 150 students participate in at least one club. That's the total number who could be picked.
- Step 3
Put the art count over the eligible total
All art students are in the eligible group. Subtract the overlap once from the combined total, but keep those students in the art count. So the probability, the art count divided by all possible picks, is
- Step 4
Write the probability as a choice
Type in Desmos. It shows ; tap the fraction button to see . So the probability that an eligible student participates in art is . Choice C.