Seven thousand raffle tickets are to be sold at $10 each to benefit a local community group. The prizes, the number of each prize to be given away, and the dollar value of winnings for each prize are as follows:

Prize Number to Be
Given Away Dollar Value
Automobile 2 $21,730
Entertainment center 5 4,191 each
DVD recorder 4 610 each
Gift certificate 55 22 each

If you buy one ticket, calculate your expected winnings. (Form the probability distribution of x = your dollar winnings, and remember to subtract the cost of your ticket.)

Any help would be greatly appriciated. Thanks

To calculate your expected winnings, you need to compute the probability distribution of the dollar winnings. The probability distribution shows the likelihood of each possible outcome and its corresponding dollar value.

First, let's find the probability for each prize:

For the automobile:
- There are 2 automobiles to be given away.
- Since there are 7,000 raffle tickets sold, the probability of winning an automobile is 2/7,000.

For the entertainment center:
- There are 5 entertainment centers to be given away.
- The probability of winning an entertainment center is 5/7,000.

For the DVD recorder:
- There are 4 DVD recorders to be given away.
- The probability of winning a DVD recorder is 4/7,000.

For the gift certificate:
- There are 55 gift certificates to be given away.
- The probability of winning a gift certificate is 55/7,000.

Next, we'll calculate the dollar amount for each possible outcome:

For the automobile, the dollar value is $21,730. Since there are 2 automobiles, the dollar winnings for the automobile prize are 2 * $21,730.

For the entertainment center, the dollar value is $4,191. The dollar winnings for the entertainment center prize are 5 * $4,191.

For the DVD recorder, the dollar value is $610. The dollar winnings for the DVD recorder prize are 4 * $610.

For the gift certificate, the dollar value is $22. The dollar winnings for the gift certificate prize are 55 * $22.

Now, let's calculate the probability distribution:

- Multiply each probability by its corresponding dollar winnings.

For the automobile:
Probability = 2/7,000
Dollar winnings = 2 * $21,730

For the entertainment center:
Probability = 5/7,000
Dollar winnings = 5 * $4,191

For the DVD recorder:
Probability = 4/7,000
Dollar winnings = 4 * $610

For the gift certificate:
Probability = 55/7,000
Dollar winnings = 55 * $22

Finally, add up the dollar winnings:

Add the dollar winnings for each prize and subtract the cost of the ticket ($10) to determine the expected winnings.

Expected winnings = (Automobile dollar winnings + Entertainment center dollar winnings + DVD recorder dollar winnings + Gift certificate dollar winnings) - $10

Now you have the expected winnings based on the probability distribution.