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

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.

14

step-by-step explanation:

14 x 3 = 42