Questions: Melinda buys one raffle ticket at the Spring Fling since there is one 1000 prize, one 500 prize, and five 100 prizes. There were a total of 800 tickets sold at 10 each. Part: 0 / 2 Part 1 of 2 (a) What is Melinda's expectation? Melinda's expectation is dollars.

Solution Steps

To find Melinda's expectation, we need to calculate the expected value of the raffle ticket. This involves multiplying the probability of winning each prize by the value of that prize and summing these products. The probability of winning a prize is the number of that prize divided by the total number of tickets.

The total number of tickets sold is \( 800 \). The probabilities of winning each prize are calculated as follows:

• For the \$1000 prize: \[ P(1000) = \frac{1}{800} \]

• For the \$500 prize: \[ P(500) = \frac{1}{800} \]

• For each \$100 prize (5 prizes): \[ P(100) = \frac{5}{800} = \frac{1}{160} \]

The expected value \( E \) is calculated by summing the products of each prize's value and its probability:

\[ E = (1000 \cdot P(1000)) + (500 \cdot P(500)) + (100 \cdot P(100) \cdot 5) \]

Substituting the probabilities:

\[ E = (1000 \cdot \frac{1}{800}) + (500 \cdot \frac{1}{800}) + (100 \cdot \frac{5}{800}) \]

Calculating each term:

\[ E = \frac{1000}{800} + \frac{500}{800} + \frac{500}{800} = \frac{1000 + 500 + 500}{800} = \frac{2000}{800} = 2.5 \]

Final Answer