A conditional probability question limits who can be selected before you calculate a chance. Wording such as selected from a group points to a table row or column: that group's total becomes the denominator. The numerator is the cell where that group meets the target. The grand total is tempting, but it includes people who cannot be picked.
Hints
- Hint 1
A condition tells you which students could still be selected. The words brought lunch from home limit the selection to one row of the table. What is the total for that row?
- Hint 2
A favorable outcome is a selected student who meets the goal. Within the lunch-from-home row, find the cell under Participates in chess club. That count goes above the row total in your fraction.
Step-by-step
Use the restricted row
Step 1Find the group that can be selected
No Desmos needed. The table gives the counts, and this fraction simplifies by hand. The student brought lunch from home, so only students in that row can be selected. Its total is , so is the denominator, not the table's .
- Step 2
Find the chess-club count in that row
In the lunch-from-home row, the chess-club column crosses at . That's the favorable count: students meet the goal and could be selected. The column total of includes students outside this row.
- Step 3
Write the probability
A probability puts the favorable count over the total that could be selected. Keep both counts in the lunch row:
The bar means “given that the student brought lunch.”
- Step 4
Simplify the fraction
Divide the numerator and denominator by , which keeps the fraction's value the same:
So the probability that a student who brought lunch participates in the chess club is . Choice C.