Question

at a college basketball game, the lucky ticket holder will win an expense - 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 randomly. the bin will hold only 400 chips. which method ensures 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 based on age. then randomly select one of the groups and place it in the bin. randomly select the winner of the trip from the bin. b. 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. c. 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. d. 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.

Explanation:

Step1: Understand the goal

The goal is to ensure each of the 4000 ticket - holders has a fair chance of winning with only 400 chips in the bin.

Step2: Analyze option A

Grouping by age is not random selection for all ticket - holders. It may introduce bias based on age.

Step3: Analyze option B

Randomly assign 4000 ticket - holders to 40 equal - sized groups and then randomly select 4 groups. Each ticket - holder has an equal chance of being in one of the selected groups. The number of ticket - holders in the selected groups is $\frac{4000}{40}\times4 = 400$. This gives each of the 4000 ticket - holders a fair chance of winning.

Step4: Analyze option C

Selecting only the first 400 ticket - holders is not fair as it does not give all 4000 ticket - holders an equal chance.

Step5: Analyze option D

Selecting from a certain section of the auditorium is not fair as it does not give all ticket - holders an equal chance.

Answer:

B. Randomly assign the 4000 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.