A small bar/casino is considering introducing a new simple card game. A price for playing the game has not been set yet, so the "winnings" below are the gross payouts from the bar/casino to the player. Assume a well shuffled standard deck of 52 playing cards

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The proposed possibilities are as follows. A single card is drawn by the player. If it is a red card or a 9, the player wins nothing. If a spade (besides the 9 of spades), the player wins $5. A club (besides the 9 of clubs) wins $10, plus an extra $100 if the card is the ace of clubs. For parts (a) - (d), assume the deck is c omplete and well shuffled before each play of the game.

a. Create the probability distribution for this game (write in tabular form), specifying all possible outcomes and their associated probabilities.

b. What is the expected value of a player's winnings for a single play of the game?

c.What is the standard deviation of a player's winnings for a single play of the game?

d.Suppose the bar/casino wants to have a 15% markup over their cost of the game, on average (assume there are no other incremental costs except the game payouts). What price should the bar/casino set for the game?