Question

A bookstore rents books to students for $2 per book. The cost of running the bookstore is $300 per hour. The numbers of books and the probabilities that the bookstore would rent them in an hour mimics the distribution of the outcomes of flipping four coins. The probability of renting a number of books was observed to be the same as the number of heads that appear in a four-coin flip. This distribution is represented in the table. Students usually rent four books a week during exams. The store manager decides to charge a weekly fee of $6 for renting an unlimited number of books. This is a decision (fair or unfair) for the students as they will pay (more than,the same as, less than) they would pay to rent four books.

Books Rented Probability
0 1/16
1 4/16
2 6/16
3 4/16
4 1/16

Answer 1

The decision to charge a weekly fee of $6 is fair for the students.

The expected cost of renting books per hour is $2.25, while the expected revenue per hour from the weekly fee is $0.86. This means that the bookstore is expected to lose money on the weekly fee, so it is a fair deal for the students.

Here is a more detailed breakdown of the calculations:

The expected cost of renting books per hour is calculated by multiplying the number of books rented by the probability of renting that number of books, and then summing the results for all possible numbers of books rented. In this case, the expected cost of renting books per hour is $2 * (0 * 1/16 + 1 * 4/16 + 2 * 6/16 + 3 * 4/16 + 4 * 1/16) = $2.25.

The expected revenue per hour from the weekly fee is calculated by dividing the weekly fee by the number of hours in a week. In this case, the expected revenue per hour from the weekly fee is $6 / 7 = $0.86.

Comparing the expected cost and revenue, we can see that the bookstore is expected to lose money on the weekly fee. This is because the expected cost of renting books per hour ($2.25) is greater than the expected revenue per hour from the weekly fee ($0.86). Therefore, the decision to charge a weekly fee of $6 is fair for the students.

Answer 2

This question seems to have way too much information and be more confusing then it needs to be. When it comes down to it the only important information is that

>The store manager decides to charge a weekly fee of $6
>Books to students for $2 per book

And the question is
>This is a decision (fair or unfair) for the students as they will pay (more than,the same as, less than) they would pay to rent four books.

Answer:
(I think) the decision is fair for the students as they will pay less than they would pay to rent four books.