Questions: QUESTION 6 - 1 POINT Leta is participating in a raffle. She purchases 10 tickets at 1 each. If she wins, she will get a 200 gift card. There are a total of 500 raffle tickets sold and only one of them is a winner. By purchasing 10 tickets, Leta ensures herself a probability of winning of 10/500. What is the expected value for Leta? Round to the nearest cent. Do not round until your final calculation. Provide your answer below:

Solution Steps

To find the expected value for Leta, we need to calculate the expected gain from the raffle. The expected value is calculated by multiplying the probability of each outcome by its corresponding value and summing these products. Leta has a probability of winning of \(\frac{10}{500}\) and a probability of losing of \(\frac{490}{500}\). If she wins, she gains $200 minus the cost of the tickets ($10), and if she loses, she loses the cost of the tickets ($10).

The probability of Leta winning the raffle is given by

\[ P(\text{win}) = \frac{10}{500} = 0.02 \]

The probability of losing is

\[ P(\text{lose}) = \frac{490}{500} = 0.98 \]

If Leta wins, her gain is

\[ \text{Gain}_{\text{win}} = 200 - 10 = 190 \]

If she loses, her loss is

\[ \text{Loss}_{\text{lose}} = -10 \]

The expected value \(E\) can be calculated using the formula:

\[ E = P(\text{win}) \cdot \text{Gain}_{\text{win}} + P(\text{lose}) \cdot \text{Loss}_{\text{lose}} \]

Substituting the values:

\[ E = (0.02 \cdot 190) + (0.98 \cdot -10) \]

Calculating this gives:

\[ E = 3.8 - 9.8 = -6.0 \]

Final Answer