The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black,

Question

The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they loose their money.

Question2 19 pts Deviatiorn Colors P(X) X*P(X) (Winnings) (X-E)21P(x) 3 Reds 2 Reds 1 Red No Reds Expected Value: Var(X): Standard Deviation:

Explanation / Answer

for 3 reds; expected winning (X)= 3 * ( 2-1 ) = $ 3

for 2 reds; Expected winning (X)= 2 * 2 - 3 = $1

for 1 reds, expected winning (X) = 1 * 2 - 3 = -$1

for 0 reds, expected winning (X) = 0 - $3 = $ 3

Here P(X=3) = 3C3 (18/38)3 = 0.1063

P(X =1) = 3C2 (18/38)2(20/38)1 = 0.3543

P(X = -1) = 3C1 (18/38)1(20/38)2 = 0.3936

P(X =-3) = 3C0 (20/38)3 = 0.1458

E(X) = -0.158

Var(X) = 2.9917

Standard Deviation = Sqrt[ Var(X)] = sqrt[2.9917] = 1.7297

Colors X P(X) X *P(X) (X - E(X))^2 * P(X) 3 Reds 3 0.1063 0.3189 1.0599 2 Reds 1 0.3543 0.3543 0.4750 1 Red -1 0.3936 -0.3936 0.2791 0 Red -3 0.1458 -0.4374 1.1777 Sum 1 -0.1579 2.9917

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