Question

At an opening for a new store, the first 50 customers are given gift certificates. There are 35 gift certificates worth $10 each, 10 gift certificates worth $15 each, 4 gift certificates worth $50 each, and 1 gift certificate worth $75. The gift certificates are handed out randomly to the first 50 customers.

Natalie is one of the first 50 customers. What is the expected value of the gift certificate that she will receive?
A.
$3.00


B.
$10.00


C.
$15.50


D.
$37.50

Answer 1

To find the expected value of the gift certificate that Natalie will receive, we will first determine the total number of gift certificates and their values.

### Count and Value of Gift Certificates:
- 35 gift certificates worth $10 each:
Value: \( 35 \times 10 = 350 \)

- 10 gift certificates worth $15 each:
Value: \( 10 \times 15 = 150 \)

- 4 gift certificates worth $50 each:
Value: \( 4 \times 50 = 200 \)

- 1 gift certificate worth $75:
Value: \( 1 \times 75 = 75 \)

### Total Number of Gift Certificates:
Total = 35 + 10 + 4 + 1 = 50

### Total Value of All Gift Certificates:
Total Value = 350 + 150 + 200 + 75 = 775

### Expected Value Calculation:
The expected value \(E\) of the gift certificate Natalie receives can be calculated as follows:

\[
E = \frac{\text{Total Value of all gift certificates}}{\text{Total number of gift certificates}}
\]
\[
E = \frac{775}{50}
\]
\[
E = 15.5
\]

Thus, the expected value of the gift certificate that Natalie will receive is **$15.50**.

### Answer:
C. $15.50