Lottery:I buy one of400raffle tickets for$10. The sponsors then randomly select1grand prize worth$500, then2second prizes worth$200each, and then10third prizes worth$50each. The selections are made without replacement.(a) Complete the probability distribution for this raffle. Give your probabilities as a decimal (rounded to 4 decimal places) or as a fraction.

Outcomes P(x)

Win Grand Prize _________

Win a Second Prize_________

Win a Third Prize _________

Win Nothing ________

(b) Recognizing that I spent$10to buy a ticket, determine the expected value of this raffle to me as a player. Round your answer to the nearest penny.

__________dollars

(c) What is an accurate interpretation of this value?

___It represents how much you would win every time you play the game.

___It represents the per-game average you would win/lose if you were to play this game many many times.

___It represents how much you would lose every time you play the game.

___It is meaningless because you can't actually win or lose this amount.