Gambler's ruin - problem 8

Probability Level 2

Notice that the wheel has 38 slots, 18 red, 18 black and two green. The wheel is spun with a ball in it. When it stops spinning, the ball comes to rest in one of the slots. All slots are equally likely.

The game works as follows:

You pay Cass a dollar, and declare a color, red or black.
Cass spins the wheel.
When the wheel stops spinning, if the ball falls into a slot of your chosen color, Cass pays you two dollars. Otherwise you get nothing.

Is this a fair game?

Yes Impossible to determine No

1 solution

Jesse Li
Feb 28, 2019

The probability of winning is less than $\frac{1}{2}$ , because 18 out of the 38 possible slots win. If the probability of winning was $\frac{1}{2}$ , then you can expect to win $\frac{1}{2} \times 2=1$ dollars, and since you already paid 1 dollar to play, that’s equivalent to breaking even. However, since the probability of winning is less than $\frac{1}{2}$ , the answer is $\boxed{No}$ .

In other words the expected value doesn't equal 0

Peter van der Linden - 2 years, 3 months ago

Gambler's ruin - problem 8

1 solution

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