The phrase “chosen from” signals conditional probability: the selection is restricted to one group. Use that group’s total as the denominator, then count the students in it who meet the second requirement. Use the selected group’s total as the denominator. Dividing by the whole school’s total answers a different question.
Hints
- Hint 1
The phrase “from those enrolled in AP Calculus” is a condition: only Calculus students can be chosen. Which count gives the size of that group, rather than the size of the whole school?
- Hint 2
The numerator counts students who meet both requirements: they’re in Calculus and Statistics. All Statistics students aren’t necessarily eligible to be chosen. Which given count tells you how many students are in both courses?
Step-by-step
Restrict the group, then divide
Step 1Choose the denominator
The words “from those enrolled in AP Calculus” make Calculus enrollment the condition, or rule for who can be chosen. So the denominator, the number of possible students, is , not all seniors.
- Step 2
Count students who meet both requirements
Of those Calculus students, are enrolled in both courses. That’s the numerator, the count who also take Statistics. The Statistics students aren’t the numerator because some may not take Calculus.
- Step 3
Write the probability
A probability is the favorable count divided by the number who could be chosen. Both counts must come from the Calculus group, so write:
The vertical bar means “given Calculus enrollment.”
- Step 4
Simplify the fraction
Type into Desmos. It shows ; tap its fraction button to see . So the probability that a chosen Calculus student also takes Statistics is . Choice B.