A friend has a new game they want you to play with them. The game is simple: the numbers 1 through 10 are written on separate identical pieces of paper and put in a bag. You are allowed to pick four numbers between 1 and 10. Your friend then randomly selects one of the pieces of paper form the bag. If the paper has one of your numbers on it you win $8, and if it has a number you didn't pick you only win $3. a) What are the two possible event outcomes of playing this game, and their associated probabilities? [2] b) Determine the expected winnings for one play at this game. [2] c) If you were to play this game 20 times, how much money should you expect to win? [1] d) Was your answer from part c) descriptive or inferential statistics? [1] e) Your friend decides that it will cost you $4.50 to play the game. Are you expecting to win money or lose money playing the game?