Three balls are randomly chosen without replacement from an urn containing 4 red, 3 white, and 3 blue balls. suppose that we win $2 for each white ball selected and lose $1 for each red selected. You win no money if a blue ball is selected. Let X denote the amount of money you have after the game.

a) Write out the pmf of X. Show how you determined this.

b) What is the probability that you lose money?

c) What is the probability that you break even (i.e. you have $0) at the end of the game?

d) Given that you won some money, what is the probability that you won at least $4?

e) What is the expected amount of money you have at the end of the game?

f) If you had to pay $1 to even start the game, would this be a good investment? Explain why or why not.