The game of European roulette involves spinning a wheel with 37 slots: 18 red, 1

Question

The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 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 thelr color, they double thelr money. If It lands on another color, they lose thelr money (a) Suppose you play roulette and bet $9 on a single round. What Is the expected value and standard deviation of your total winnings? (Round your answers to the nearest cent.) expected value standard deviation (b) Suppose you bet $3 in three different rounds. What is the expected value and standard deviation of your total winnings? expected value standard deviation $ (c) How do your answers to parts (a) and (b) compare? What does this say about the riskiness of the two games? The expected value of playing a single round is-Select- the expected value of playing three different rounds. The standard deviation of playing a single round is-select- the expected value of playing three different rounds. Therefore, there is-Select- risk playing once with $9 than playing three times with $3.

Explanation / Answer

a) here probabilityof winning P(X=9) =18/37

probability of losing =P(X=-9) =19/37

therefore from above:

expected value: E(X) =-0.24

std deviation =(E(X2)-(E(X))2)1/2 =(81-(-0.24)2)1/2 =9.00

b)

as above:

tehrefore expected value =3*(-0.08) =-0.24

std deviaiton =5.19 ( please try 5.20 if this does not work due to rounding_)

c)

expected.....single round is same ............

std deviaiton.....is different..........

there is high risk ......

please revert for any clarification required

x P(x) xP(x) x^2P(x) 9 18/37 4.38 39.41 -9 19/37 -4.62 41.59 total 1.00 -0.24 81.00

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