Ten thousand raffle tickets are sold. 1 first prize of $1800, 3 second prizes of $600 each, and 9 third

prizes of $200 each are to be awarded, with all winners selected randomly. If you purchase one
ticket, what are your expected winnings?

To calculate your expected winnings, you need to find the probability of winning each prize and multiply it by the amount of each prize.

First, let's find the probability of winning the first prize:
There is only 1 first prize, and since 10,000 tickets are sold, the probability of winning the first prize is 1/10,000.

The second prize has 3 winners, so the probability of winning a second prize is 3/10,000.

Similarly, the probability of winning a third prize is 9/10,000, as there are 9 third prizes.

Now, let's calculate the expected winnings:

Expected winnings = (Probability of winning the first prize * Amount of the first prize) +
(Probability of winning a second prize * Amount of a second prize) +
(Probability of winning a third prize * Amount of a third prize)

Expected winnings = (1/10,000 * $1800) + (3/10,000 * $600) + (9/10,000 * $200)

Calculating this expression:

Expected winnings = ($1800/10,000) + ($1800/10,000) + ($1800/10,000)

Expected winnings = $5400/10,000

Simplifying, we get:

Expected winnings = $0.54

Therefore, if you purchase one ticket, your expected winnings are $0.54.