In a two-way table, conditional probability means finding a probability within a group the question has already specified. Wording such as selected from or who walks tells you which row or column becomes the whole group. Find its total, then find the cell that also matches the target. Divide by the restricted total, not by everyone surveyed.
Hints
- Hint 1
A condition is something already known about the selected student. The phrase who walks to school rules out everyone who doesn't walk. Which column contains all the students who could be picked?
- Hint 2
A column total includes both grades in that column. Add both walker counts for the denominator, then find the grade 7 count within that same column for the numerator.
Step-by-step
Restrict to the walkers
Step 1Choose who can be selected
The phrase who walks to school is the condition: something already true about the selected student. Only walkers can be picked, so the walkers column is the new whole. The surveyed students include people who can't be selected.
- Step 2
Find the walkers' total
The walkers column has grade 7 students and grade 8 students. Type in Desmos; it shows . So walkers could be selected. This is the denominator, the bottom of the probability fraction.
- Step 3
Find the matching students
Read across the grade 7 row to the walkers column. That cell contains students. They're the favorable outcomes, the walkers who match the grade the question asks for.
- Step 4
Write the probability
Put the favorable count over the number who could be selected:
The bar means “given that.” Keep on the bottom because the student is picked from the walkers, not from all students.
- Step 5
Match the fraction to a choice
Type on a new Desmos line. It shows about ; use the fraction button to see . So the probability that a selected walker is in grade 7 is . Choice A.