In a new card game, you start with a well-shuffled full deck and draw 3 cards without replacement. If you draw 3 hearts, you win $50. If you draw 3 black cards, you win $25. For any other draws, you win nothing.
(a) Find the expected winnings for a single game.
(b) Find the standard deviation of the winnings.
(c) If the game costs $5 to play, what would be the expected value of the net profit (or loss)?
(Hint: profit = winnings - cost; X - 5)
(d) If the game costs $5 to play, what would be the standard deviation of the net profit (or loss)?
(e) If the game costs $5 to play, should you play this game?