In a conditional probability question, wording that selects someone from a particular group makes that group the whole pool. In a two-way table, add the counts in that group’s row or column for the denominator, then use the requested count within it for the numerator. Type the fraction into Desmos to check it. Including people outside the selected group changes the question.
Hints
- Hint 1
The condition is what you already know about the selected student. Only grade 8 students can be picked, so which two cells make up the total number of possible students?
- Hint 2
The numerator counts students who meet the club requirement. Find that count within grade 8, then divide it by the grade 8 total.
Step-by-step
Count within the selected grade
Step 1Find the eligible group
The condition “one student in grade 8” means only the grade 8 row can be selected. It has robotics students and art students. Type in Desmos; it shows , the total number of eligible students. Don’t include grade 9 in that total.
- Step 2
Find the probability within that group
Of those grade 8 students, signed up for robotics. Probability is the favorable count divided by the eligible total, so type on the next Desmos line. It shows ; use the fraction button to see . The probability that the selected grade 8 student signed up for robotics is . Choice B.