Question

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 $2 on the Joker denomination, find the player's expectation. (Round your answer to two decimal places.)

Answer 1

Solution:

The denominations and the corresponding slots for the big six money wheel is given as follows:

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

there are 54 slots.

It is given that a player bets $2 on the Joker denomination.

It is given that it is a $2 bet

If a person gets the Joker denomination the amount he wins is given as follows:

Amount he wins = $ 40 * 2

= $ 80

If a prson does not get a Joker denomination ,he loses $2.

The propability of getting a Joker deomination is , p = 1/ 54

The Probability of not getting a Joker denomination, q = 53/54

The players expectation is given as follows:

E(X) =(Amount he wins) * p-(Amount he loses)*q

= ( 80* ( 1/54)) - ( 2 * (53/54))

= -0.481481

Hence, the player is expected to lose $ 0.481481.

Therefore,the player's expectation is -$0.481481