Lottery Prizes A lottery offers one 1000 prize, two 500 prizes, three 400 prizes, and five 200 prizes. One thousand tickets are sold at 5$ each. Find the expectation if a person buys four tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.

The expectation if a person buys four tickets is____
dollar(s).

To find the expectation if a person buys four tickets in the given lottery, we need to calculate the sum of the expected values for each individual ticket and then multiply it by four since the person is buying four tickets.

Let's calculate the expected value for each type of prize:

1. $1000 prize: The probability of winning this prize is 1/1000 since there is only one such prize out of 1000 tickets. Therefore, the expected value of this prize is (1/1000) * $1000 = $1.

2. $500 prizes: The probability of winning each of the two $500 prizes is 2/1000 since there are two such prizes out of 1000 tickets. Therefore, the expected value of each $500 prize is (2/1000) * $500 = $1.

3. $400 prizes: The probability of winning each of the three $400 prizes is 3/1000 since there are three such prizes out of 1000 tickets. Therefore, the expected value of each $400 prize is (3/1000) * $400 = $1.20.

4. $200 prizes: The probability of winning each of the five $200 prizes is 5/1000 since there are five such prizes out of 1000 tickets. Therefore, the expected value of each $200 prize is (5/1000) * $200 = $1.

Now, let's calculate the overall expected value for each individual ticket by summing up the expected values for all types of prizes:

Expected value per ticket = $1 + $1 + $1.20 + $1 = $4.20

Since the person is buying four tickets, we can calculate the overall expected value for the person:

Overall expected value = Expected value per ticket * Number of tickets bought = $4.20 * 4 = $16.80

Therefore, the expectation if a person buys four tickets in this lottery is $16.80.