Suppose that a deck with all the face cards (Ace, King, Queen and Jack) removed,

Question

Suppose that a deck with all the face cards (Ace, King, Queen and Jack) removed, is used to determine a money payoff, e.g., a draw of a 2 of clubs would pay $2, a draw of a 10 of diamonds would pay $10, and so on. 1. a. Write the nine possible money payoffs and the probability associated with b. What is the expected value of a single draw from the deck, assuming that it c How much money would you pay to play this game? each has been well shuffled? d. Based on your answer to part (c), would you are preferences for this game be characterized as risk averse, risk neutral, or risk loving? Make sure to justify your answer.

Explanation / Answer

a) Here we have only the card with ranks from 2 to 10. Therefore there are 4 cards for each of the 9 ranks possible here. Therefore, we get:

P(X = 2) = P(X = 3) = P(X = 4) = P(X = 5) = P(X = 6) = P(X = 7) = P(X = 8) = P(X = 9) = P(X = 10) = 1/9

b) The expected value of X here is computed as the average value of the 9 ranks above as all of those 9 ranks are equally likely. Therefore, we get:

E(X) = (2 + 3 + 4 + ....... + 10 ) / 9

E(X) = 6

Therefore the expected value of the payoff here is 6

c) I would be ready to pay amount less than the expected value that is less than 6 for example I would be ready to pay 5 to play the game.

d) Based on the previous part, I am a risk averse person because I am only ready to pay less than the expected payoff from the game.

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