In the game of roulette, a player can place a $4 bet on the number 23 and have a StartFraction 1 Over 38 EndFraction probability of winning. If the metal ball lands on 23, the player gets to keep the $4 paid to play the game and the player is awarded an additional $140. Otherwise, the player is awarded nothing and the casino takes the player's $4. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?

a.The expected value of the game to the player is -$0.2105

b. The player should expect to lose $210.50¢ if he/she places the bet or plays the game 1,000 times

Step-by-step explanation:

Please kindly check the attached files for explanation.

First: Reflect across the Y axis:

A moves to (4,4)

B moves to (2,2)

C moves to (2,-1)

D moves to (4,1)

Second and final transition, shift down 3 units

A' becomes (4,1)

B' becomes (2,-1)

C' becomes (2,-4)

D' becomes (4,-2)

B) yes they are congruent, because the shape did not change size, just location and orientation.