The Roulette wheel has 38 slots numbered from 1 to 36, 0, and 00.For the slots l

Question

The Roulette wheel has 38 slots numbered from 1 to 36, 0, and 00.For the slots labelled 1-36,

half are coloured red and half black. The remaining two slotsare both green. The wheel is

spun, and a ball is thrown into the wheel and lands in one of theslots. If you do not know

this game, do not worry. It is sufficient to understand thatthe ball lands on one of the

coloured numbers or you can use the web to figure the gameout.

It costs $1 to bet on the group of numbers 1-12. If the ball doesnot land on the values from 1-

12, the person loses the bet. If the ball does land on one of thesenumbers, the person gets

back $3.

a. What is the probability distribution for the net monetaryoutcome from the gambler’s

point of view for a $1 bet (note: the gambler spends $1 to play thegame, so a dollar

is lost when they lose)?

b. Compute the expected return of this game from thegambler’s point of view (note: the

gambler spends $1 to play the game).

c. What is the average return to the casino from 1,000,000 suchbets?

Explanation / Answer

40 spots on wheel a) $2 (3-1) if 1-12 come up P = 12/40 = 3/10 = .3 -$1 (0-1) if any thig else comes up P - 28/40 = 7/10 = .7 b) Expected return = 2(.3) + -1(.7) = -.10 (lose a dime) c) 1000000*(-.10) = $100,000

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