Consider the following card game with a well-shuffled deck of cards. If you draw

Question

Consider the following card game with a well-shuffled deck of cards. If you draw a red card, you win nothing. If you get a spade, you win $4. For any club, you win $8 plus an extra $20 for the ace of clubs, (a) Create a probability model for the amount you win at this game. (Round your answers to two decimal places.) P(x) x P(x)(x E(x))2 (x E(x)) P(x) Event Red Enter an exact number Spade Club Ace of clubs Also, find the expected winnings for a single game and the standard deviation of the winnings. (Round your answers to two decimal places.) expected winnings standard deviation (b) What is the maximum amount you would be willing to pay to play this game? Explain your reasoning If the goal of the game is making money, the maximum amount you should be willing to pay for this game is s

Explanation / Answer

here as there are 26 cards for red ; spade and 12 for club without ace and 1 for ace of clubs out of 52 cards

a)

expected value =3.38

std deviation =(22.39)1/2 =4.73

b)

for fair game =cost of game =expeted value =$3.38

x P(x) xP(x) (x-(E(X))^2 (x-(E(X))^2.P(x) red 0.00 0.50 0.00 11.46 5.73 spade 4.00 0.25 1.00 0.38 0.09 club 8.00 0.23 1.85 21.30 4.92 ace of clubs 28.00 0.02 0.54 605.92 11.65 Total 1.00 3.38 22.39

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