A conditional probability question limits who can be picked with wording like “selected from among” a group. In a two-way table, use that group’s row or column total as the denominator. Then find the cell where the group meets the target for the numerator. Using the table’s grand total ignores the limit on who can be picked.
Hints
- Hint 1
The words “one of the senior members” limit the sample space, the people who could be selected. The denominator counts only those people. Which total belongs to the senior row?
- Hint 2
A numerator counts the people who meet the target within the selected group. In the senior row, which cell shows members who participate in a sport?
Step-by-step
Use the senior row
Step 1Choose the group that can be selected
No Desmos needed. Both counts come directly from the table. The phrase “one of the senior members” is the condition: only seniors can be picked. So the Senior row’s total, , is the denominator, or the number of possible picks. Choose the denominator from the group that can be selected.
- Step 2
Count the seniors who play a sport
In the Senior row, the “Participates in a sport” cell is . That’s the numerator, the count of selected-group members who meet the target. The sports column’s total includes juniors, so it isn’t the count to use here.
- Step 3
Write the fraction
Put the seniors who play a sport over all seniors: . That’s the fraction of senior members who participate in a school sport. Choice C.