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Suppose we play the following game. You select 3 cards from a standard deck of 5

ID: 3233195 • Letter: S

Question

Suppose we play the following game. You select 3 cards from a standard deck of 52 cards. If you have no face cards, you pay me $2. If you have exactly one face card, you pay me $1. If you have exactly two face cards, I pay you $2. If you have three face cards, I pay you $9. Let X represent your net profit or loss in this game. Find the expected value of X to the nearest cent. (hint: the probabilities for selecting 0,1,2,3 cards are listed below)

(Answer Format: Do not write $ sign. Example: If answer is $1.24, enter 1.24. If answer is -$.71, enter -0.71)

x 0 1 2 3 p 0.4471 0.4235 0.1195 0.01

Explanation / Answer

with above given probability expected value of X =-0.99

x p outcome(Y) p*Y 0 0.4471 -2 -0.8942 1 0.4235 -1 -0.4235 2 0.1195 2 0.239 3 0.01 9 0.09 total -0.99