Question

select the correct answer.
at a college basketball game, one lucky ticket holder will win an all - expenses - paid trip to the conference championship game. there are 4,000 ticket holders at the game. the organizers want to place chips, each labeled with the seat number of a ticket holder, in a bin and draw the winner from the bin. unfortunately, the bin will hold only 400 chips.
which method assures both that the organizers can use the bin for the drawing and that each ticket holder will have a fair chance of winning?
a. place chips labeled with the seat numbers of each ticket holder into 10 groups and place it in the bin. then randomly select the winner of the trip from the bin.
b. place 400 chips labeled with the seat numbers of the first 400 ticket holders into the bin, and randomly select the winner of the trip from the bin.
c. place 400 chips labeled with the seat numbers of ticket holders from a certain section of the auditorium into the bin, and randomly select the winner of the trip from the bin.
d. randomly assign the 4,000 ticket holders to 40 equal - sized groups. then randomly select 4 of the groups and place their seat numbers in the bin. randomly select the winner of the trip from the bin.

Explanation:

To ensure fairness (each ticket holder has an equal chance) and use the bin (which holds 400 chips), we analyze each option:

• Option A: Grouping by age (a non - random factor) creates unequal groups, so chances aren't fair.
• Option B: Using only the first 400 ticket holders excludes the other 3600, so not all have a chance.
• Option C: Selecting from a "certain section" excludes other sections, so not all have a chance.
• Option D: First, randomly assign 4000 ticket holders to 40 equal - sized groups (4000/40 = 100 per group). Then, randomly select 4 groups (4*100 = 400), and place their seat numbers in the bin. This way, every ticket holder has an equal chance of being in the selected groups (and thus having their number in the bin), and the bin is used with 400 chips.

Answer:

D. Randomly assign the 4,000 ticket holders to 40 equal - sized groups. Then randomly select 4 of the groups and place their seat numbers in the bin. Randomly select the winner of the trip from the bin.