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.

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




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 (fair,unfair)decision for the students as they will pay (more than, less than, the same as)they would pay to rent four books.

Answer 1

fair
less than
this is the answers.

Answer 2

Fair decision for the students as they will pay less than they would pay to rent four books.

Explanation:

the distribution represented in the table as follow:

Books Rented Probability

0 1/16

1 4/16

2 6/16

3 4/16

4 1/16

The expected amount spent by the students is given by:

`0* (1)/(6)+1* (4)/(16)+2* (6)/(16)+3* (4)/(16)+4* (1)/(16)`

`0+(4)/(16)+(12)/(16)+ (12)/(16)+ (4)/(16)`

On solving we get,

`(32)/(16)`=$2

Therefore, the amount spent by students is $2

This is a fair less than they would pay to rent four books.