A random pick restricted to one group is a conditional probability question: you’re finding a chance within that group. First identify who can be picked, then count how many of those people have the trait you want. The group being picked from sets the denominator. Dividing by the original total ignores the restriction.
Hints
- Hint 1
A condition is something you already know about the selected student. The phrase who chose a fiction book limits who can be picked. How many students are in that smaller group?
- Hint 2
The numerator counts the outcomes you want. Keep it inside the fiction group: how many of the students who chose fiction also joined the book club?
Step-by-step
Count within the fiction group
Step 1Find the group that can be selected
No Desmos needed. The counts give the probability directly.
The student is selected from the fiction readers, so no nonfiction reader can be picked. The denominator, the total number of possible picks, is fiction readers, not all students.
- Step 2
Count book-club members in that group
Of those fiction readers, joined the club. That’s the numerator, the count of picks you want. So the probability within the fiction group is
The chance that a selected fiction reader joined the club is . Choice B.