9. (10 points) You are the manager of a casino and have a game where the player

Question

9. (10 points) You are the manager of a casino and have a game where the player puts down a bet. Then the player draws a card at random from a standard 52 card deck. If the player picks an A to 5, then he wins $5 and keeps his bet. If the player picks a 6 to 10, then the player wins $10 and keeps his bet. If the player picks a face card (K, Q, J), then the player wins nothing and loses his bet. What should the amount of the required bet B be in order for the expected value (E) of the to be zero? x = card drawn P(x) Payoff(x) P(x)*Payoff(x) K -B Q J 10 9 8 7 6 5 4 3 2 A or 1 Sums to 1 E =

Explanation / Answer

let the the amount of the required bet B = x

cards    payment

A-5 - 5

6-10 -    10

face card -    -x

5/13 * 5 + 5/13 *10 - x*3/13 = 0

25 + 50 =3x

75 = 3x

x = 25

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