A conditional probability is a chance calculated within a group the question has already specified. In a two-way table, the phrase “selected from” tells you which row or column total belongs on the bottom of the fraction. Then find the target count inside that same group. Don’t use the table’s grand total when some people cannot be picked.
Hints
- Hint 1
The selection group contains only students who could be picked. In a two-way table, a column total counts everyone in that column. Which column matches the group the question selects from?
- Hint 2
An intersection is the cell where a row and column meet. Find where the Design row meets the Saturday column. That count goes on top of the probability fraction, not the Design row total.
Step-by-step
Restrict the group, then count
Step 1Find the group that can be picked
The student is selected from those who chose Saturday, so only the Saturday column counts. Its total is . The group you pick from sets the denominator, the bottom of the probability fraction. The table’s includes Sunday students who cannot be picked.
- Step 2
Find the design students in that group
Look where the Design row meets the Saturday column. That intersection, the cell shared by both categories, is . So Saturday students selected design.
- Step 3
Write the probability
Put the design students over all students who could be picked. In conditional probability notation, the bar means “given Saturday”:
- Step 4
Evaluate the fraction
Type in Desmos. It displays ; tap its fraction button to see . So the probability that a Saturday student selected design is . Choice A.