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

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 slots are both green. The wheel is
spun, and a ball is thrown into the wheel and lands in one of the slots. If you do not know
this game, do not worry. It is sufficient to understand that the ball lands on one of the
coloured numbers or you can use the web to figure the game out.
It costs $1 to bet on the group of numbers 1-12. If the ball does not land on the values from 1-
12, the person loses the bet. If the ball does land on one of these numbers, the person gets
back $3.
a. What is the probability distribution for the net monetary outcome from the gambler’s
point of view for a $1 bet (note: the gambler spends $1 to play the game, so a dollar
is lost when they lose)?
b. Compute the expected return of this game from the gambler’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 such bets?

Explanation / Answer

Win $2 (3-1) 12/38 or 6/19 Lose $1 26/38 or 13/19 Expected return 2*6/19- 1*13/19= -1/19 Return to casino 1,000,000 * 1/19= 52,631.58

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