A roulette wheel used in a U. S. casino has 38 slots of which 18 are red, 18 are black, and 2 are green. A roulette wheel used in a French casino has 37 slots, of which 18 are red, 18 are black, and 1 is green. A ball is rolled around the wheel and ends up in one of the slots with equal probability. Suppose that a player bets on red. If a $1 bet is placed, the player wins $1 if the ball ends up in a red slot. (The player’s $1 bet is returned.) If the ball ends up in a black or green slot, the player loses $1. Find the expected value of this game to the player in a. The United States. b. France.

(a) - $0.0526

(b) - $0.0270

Step-by-step explanation:

(a) In the United States

Total roulette slots = 38 slots, red = 18 slots, black = 18 slots, green = 2

If ball lands in the red slot, the player wins $ 1. If the ball lands in the black or green slot, the player loses $ 1.

Probability = number of events ÷ possible outcome

P (win) = P (red) = number of red slots ÷ total number of slots

P (red) = 18 ÷ 38 = 9/19

P (red) = 9/19

P (loss) = P (black or green) = number of green or black slots ÷ total number of slots

P (black or green) = P (black) + P (green) = (18 + 2) ÷ 38 = 20 ÷ 38

P (black or green) = 10/19

Expected value = sum of all (possible outcome x probability) = Value of win + Value of loss

Expected value = 1 * (9/19) + (-1) * (10/19) = (9/19) - (10/19)

Expected value = - (1/19) = - $0.0526

(b) In France

Total roulette slots = 37 slots, red = 18 slots, black = 18 slots, green = 1

If ball lands in the red slot, the player wins $ 1. If the ball lands in the black or green slot, the player loses $ 1.

Probability = number of events ÷ possible outcome

P (win) = P (red) = number of red slots ÷ total number of slots

P (red) = 18 ÷ 37 = 18/37

P (red) = 18/37

P (loss) = P (black or green) = number of green or black slots ÷ total number of slots

P (black or green) = P (black) + P (green) = (18 + 1) ÷ 37 = 19 ÷ 37

P (black or green) = 19/37

Expected value = sum of all (possible outcome x probability) = Value of win + Value of loss

Expected value = 1 * (18/37) + (-1) * (19/37) = (18/37) - (19/37)

Expected value = - (1/37) = - $0.0270

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong

median is the value separating the higher half of a data sample, a population or probablity distribution from the lower half.

step-by-step explanation:

say you have 3,8,7,3,1,9,8 order them from lowest to highest

if orderd it would be 1,3,3,7,8,8,9 now you take away from the lowest and the highest until you end up in the middle.

so you would remove the 1 and 9 leaving you with 5 digits remaining

when you've reached the middle that would be your answer so in this case the answer is 7

if there were two numbers left say 7 and 5 you'd and them together so 12 then divide by 2 witch would equal 6 so the answer would be 6

good luck on that project hoped i you at all