Create a probability distribution model (table) for the scenario below and answe

Question

Create a probability distribution model (table) for the scenario below and answer the following questions.

27) All diamonds are removed from a deck of cards and these 13 cards are placed in a bag. The cards are mixed up, and then one card is chosen at random. The player wins according to the following rules: • Pay $10 to play If the ace is drawn, the player wins $0 If a face card is drawn, the player wins $20 If any other card is drawn (2-10), the player wins $2 Outcome Probability a) Find the expected value for this game b) Find the standard deviation c) Is the game fair for the player and the owner? If it is not how much should the game cost to be fair?

Explanation / Answer

as when ace comes expected value =gain-ticket cost =0-10=-10

hence P(X=-10)=3/39=1/13 (as there are 3 aces out of 39)

for face card; P(X=20-10=10)=9/39=3/13 (as there are 9 face cards out of 39)

for other cards; P(X=2-10=-8) =27/39=9/13 as there are 27 other cards out of 39)

hence

a)

from above expected value =-0.31

b) std deviation =5.0136

c) as expected value is negative therefore game is not fair,

for game to fair cost of play =10-0.31=$9.69

outcome probability -10 1/13 10 3/13 -8 9/13

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