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Three balls are randomly chosen (without replacement) from an urn containing 3 red, 4 white, and 5 blue balls. Suppose that you will win $3 for each white ball selected and lose $2 for each red selected. You win $0 for each blue ball 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 come break even (i.e. you have $0) at the end of game?
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d) What is the probability that you win at least $5?
e) Given that you won some money, what is the probability that you won at most $4?
f) What is the expected amount of money you have at the end of the game?
g) If you had to pay $1 to play the game, would this be a good investment? Explain why or why not.
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