A roulette wheel is divided into 38 pockets. 18 are numbered red pockets, 18 are

Question

A roulette wheel is divided into 38 pockets. 18 are numbered red

pockets, 18 are numbered black pockets and 2 are green pockets.

You can place bets on specific red or black pockets with odds of

35:1. That is, if you are correct you win $35 (plus the dollar you

bet), and if you are incorrect, you lose the dollar you bet. A ball

is spun into the wheel, and we will assume it lands in all pockets

with equal probability. Your friend has developed what she

describes as a “foolproof system” for winning. It involves her

betting on $1 on 7 red again and again. You try to discourage

her, but she is insistent.

Compute the expected value, variance, and stan-

dard deviation of your friend’s net earnings after 70 spins

of the wheel.

Explanation / Answer

here probability of winning =1/38

and probability of losing =37/38

therefore

frm above expected value after 70 spins =70*(-0.05)=-$3.68 (for rounding abve it shold be -$3.50)

variance =70*33.21=2324.54

and std deviation=(2324.5)1/2 =48.21

outcome(x) p(x) xP(x) x2P(x) (x-)2 (x-)2P(x) 35 1/38 0.921 32.237 1228.687 32.334 -1 37/38 -0.974 0.974 0.898 0.874 total 1 = -0.05 33.211 1229.584 2= 33.21 std deviation=     =    2 = 5.76

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