A conditional probability question tells you that the person is selected from a particular group. In a two-way table, use that group’s entire row or column as the new total, then find the cell that also matches the requested trait. Enter the matching count over the group total in Desmos. Using the survey’s grand total answers a different question.
Hints
- Hint 1
Being selected from students who play sports is a condition: it limits who could be chosen before you ask about music lessons. Which row contains everyone who could be picked?
- Hint 2
Add both cells in the sports row, including students who don’t attend music lessons. That sum is the total number of possible picks, not the number who meet the music target.
- Hint 3
The intersection is the cell where the sports row meets the music-lessons column. Use that cell as the matching count over the sports-row total.
Step-by-step
Use the sports row as the total
Step 1Find the group that can be picked
The phrase “plays sports” is a condition, something already known about the selected student. So only students in the sports row can be picked. Type in Desmos; it shows sports players. Restrict the possible picks before counting the target.
- Step 2
Find the matching count
The student must also attend music lessons, so read where the sports row meets the music-lessons column: . Probability is the matching count divided by all possible picks, giving . The survey total of includes students who cannot be picked here.
- Step 3
Calculate the probability
Type below in Desmos. It shows ; tap the fraction button to read . So among sports players, the probability of attending music lessons is . Choice A.