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 two 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 $15, and if it has a number you didn't pick you only win $4.

a) What are the two possible event outcomes of playing this game, and their associated probabilities?

b) Determine the expected winnings for one play at this game.

c) If you were to play this game 20 times, how much money should you expect to win?

d) Was your answer from part c) descriptive or inferential statistics?

e) Your friend decides that it will cost you $6 to play the game. Are you expecting to win money or lose money playing the game?