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Spinning the Roulette Wheel and the Law of Large Numbers

APSTAT-ELVIDY

In the game of American roulette, a small ball will randomly land inside one of $38$ colored and numbered pockets on a spinning wheel. Two of these numbered pockets are green, $18$ are red, and $18$ are black. In a large casino, the wheel is spun several hundred times per day.

Based on the Law of Large Numbers, which of the following situations is most likely to occur?

A

$2$ out of the first $38$ spins of the wheel on any given day should result in the ball landing in a green pocket.

B

Approximately $5.3\%$ of all spins of the wheel during the year should result in the ball landing in a green pocket.

C

The probability that the ball will land in a green pocket on any given spin of the wheel is $1/19$.

D

Approximately $1/19$ of the spins of the wheel on any given day should result in the ball landing in a green pocket.

E

On any given spin of the wheel, approximately $5.3\%$ of people who bet that the ball will land in a green pocket will win their bet.