You play a game where you draw from a well-shuffled standarddeck of cards. If yo

Question

You play a game where you draw from a well-shuffled standarddeck of cards. If you draw a face card (Jack, Queen, or King), youwin $3. Otherwise, you lose $1. A) Draw the box model and calculate the expected value for asingle play of this game. Is this game fair? B) How many plays would you have a better chance of coming outahead with, 25 or 100 times? C) Suppose you play this game 100 times. What do you expect tomake, and how far off are you likely to be? You play a game where you draw from a well-shuffled standarddeck of cards. If you draw a face card (Jack, Queen, or King), youwin $3. Otherwise, you lose $1. A) Draw the box model and calculate the expected value for asingle play of this game. Is this game fair? B) How many plays would you have a better chance of coming outahead with, 25 or 100 times? C) Suppose you play this game 100 times. What do you expect tomake, and how far off are you likely to be?

Explanation / Answer

x (value of winnings) x (value of winnings) Pr[x] x*Pr[x] $3 12/52 36/52 -$1 40/52 -40/52 = 1 E[x] = -4/52 ˜ -$0.077 cents pergame

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