A fitness center offered new members either a monthly membership or a yearly membership.
- 80% of the new members chose the monthly membership, and the remaining 20% chose the yearly membership.
- Of the members who chose the monthly membership, 30% also enrolled in the automatic payment option.
- Of the members who chose the yearly membership, 70% also enrolled in the automatic payment option.
Based on this information, which of the following statements is supported?
The phrase “of the members who” signals a conditional probability: a chance measured within a named group. To decide which group is more likely to enroll, compare the automatic-payment rates within the two plans. The percentages choosing each plan describe group sizes, not individual enrollment chances. A larger group can have more enrollees even if its members are less likely to enroll.
Hints
- Hint 1
A conditional probability uses one specified group as its whole. “Of the members who chose the monthly membership” means the monthly members are the whole for that enrollment rate. What group is the whole for the other rate?
- Hint 2
“More likely” asks for the higher chance within a plan, not the plan with more members. Compare the two automatic-payment rates given for monthly and yearly members.
Step-by-step
Compare the rates within each plan
Step 1Identify what each percentage measures
No Desmos needed. The given rates answer the comparison directly. The phrase “of the members who” makes each plan its own whole: of monthly members and of yearly members enrolled in automatic payment. These are conditional probabilities, or chances within specified groups. The and instead tell you how many members chose each plan.
- Step 2
Compare the enrollment chances
Compare the within-plan rates: . So yearly members were more likely than monthly members to enroll in automatic payment. Compare chances within the named groups, not the sizes of those groups. Choice B.