Question

A bookstore rents books to students for $2 per book. The cost per hour of running the bookstore is $300. 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 number of books rented 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. No. of Heads Probability: 0 (1/16), 1 (4/16), 2 (6/16), 3 (4/16), 4 (1/16). Given the data in the table, what is the expected number of books rented in one hour?

A) 1
B) 2
C) 3
D) 4

Answer 1

The expected number of books rented in one hour, based on the given probability distribution of flipping four coins, is calculated to be 2.

Step-by-step explanation:

The expected number of books rented can be calculated using the probability distribution of the outcomes of flipping four coins, which is analogous to the number of books rented per hour. We calculate this expected value by multiplying each number of books rented by its respective probability and summing up these products.

1. Multiply 0 books by its probability (1/16).
2. Multiply 1 book by its probability (4/16).
3. Multiply 2 books by its probability (6/16).
4. Multiply 3 books by its probability (4/16).
5. Multiply 4 books by its probability (1/16).

Now, add up all these products to find the expected number of books rented in one hour.

Expected value = (0 × 1/16) + (1 × 4/16) + (2 × 6/16) + (3 × 4/16) + (4 × 1/16)

Expected value = (0) + (4/16) + (12/16) + (12/16) + (4/16)

Expected value = 32/16

Expected value = 2