The phrase if the student chosen knows French signals conditional probability: the pick is limited to students who know French. Use that group's total as the denominator and the matching table cell as the numerator. Add the counts in the conditioned row, then divide its study-abroad count by that total. Using the study-abroad column total instead flips the condition.
Hints
- Hint 1
In conditional probability, the condition limits who could be picked. Knows French keeps only one row of the table. What total do you get by adding the two counts in that row?
- Hint 2
The numerator counts the students you want within the allowed group. Which cell lies in both the knows French row and the study-abroad column?
Step-by-step
Restrict to the French row
Step 1Find the group that could be chosen
The condition knows French keeps only that row. It has students in the program and outside it. Type in Desmos; it shows . So is the denominator, the number of students who could be chosen.
- Step 2
Write the probability within that group
The target is enrolled in the study-abroad program, so use the where that column crosses the French row. In conditional probability, divide the target count by the conditioned group's total: . The bar means “given that.” Using the program column's total instead would reverse the condition.
- Step 3
Simplify and answer
Type on a new Desmos line. It shows about ; tap the fraction button to see . So the probability that a student who knows French is in the study-abroad program is . Choice B.