A two-way table plus information already known about the selected person signals conditional probability. The known fact shrinks the group you can pick from. Use that group’s row or column total as the denominator, then count the target where it crosses that group. Dividing by the table’s grand total answers a different question; Desmos can simplify the fraction.
Hints
- Hint 1
A condition is a fact already known about the student. Only late arrivals are possible selections now. Which total in the table counts those students?
- Hint 2
The intersection is the cell where a row and column meet. Find where Walk meets Arrived late to count walkers inside the late group, rather than using the total for all walkers.
- Hint 3
A probability is the target count divided by the total that could be selected. Put the walk-and-late cell over the late-column total, not over the total for the whole school.
Step-by-step
Restrict to the late arrivals
Step 1Choose the group that can be selected
The phrase “known to have arrived late” is a condition: a fact already fixed about the student. So only the Arrived late column is possible. Its total is , not the grand total of .
- Step 2
Count the walkers in that group
The intersection, where the Walk row meets the Arrived late column, contains students. Those are the late arrivals who walked. The Walk row total of also includes students who weren’t late.
- Step 3
Write target over restricted total
Conditional probability means the chance of walking given that the student is late; the bar in means “given that.” Use the restricted group for both the target count and the total. So .
- Step 4
Simplify the fraction
Type in Desmos. It shows ; click the fraction button to see . So the probability that a late student walked to school is . Choice D.