Question

# Many casinos have a game called the Big Six Money Wheel, which has 54 slots in...

Many casinos have a game called the Big Six Money Wheel, which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts, as shown in the table at the top of the next column. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player's bet, the player wins that amount for each dollar bet.

Denomination    Number of slots
\$40 (Joker)     ---------> 1
\$40 (Casino logo) ->    1
\$20     --------------------> 2
\$10     --------------------> 4
\$5 -----------------------> 7
\$2 -----------------------> 15
\$1    -----------------------> 24

If a player bets \$5 on the \$5 denomination, find the player's expectation. (Round your answer to two decimal places)

Given : The Big Six Money Wheel has 54 slots and the slots are as mentioned below

 Denomination Number of Slots \$40 (Joker) 1 \$40 (Casino logo) 1 \$20 2 \$10 4 \$5 7 \$2 15 \$1 24

Solution :

Player bets \$5 on the \$5 Denomination

Therefore, if he wins then he will win amount 5*5 = \$25

But if he loses then the amount lost is \$5.

The probability of getting \$5 denomination (x) = 7/54

The probability of not getting \$5 denomination (y) = 47/54

The player's expectation can be calculated as,

E(Player) = (Amount won) (x) - (Amount lost)(y)

= (25)(7/54) - (5)(47/54)

= 3.24 - 4.35

= -1.11

Therefore, the player's expectation is -\$1.11

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