What is the Probability of Winning with Consecutive Spins on a Roulette Wheel?

[Ivan91]

So, I have a very easy question.
Imagine a roulette with 38 pockets (0,00,1,2,3,...36)
Suppose you were to place bets on numbers 1,2,3,4.
What is the probability that at least one of your numbers would be the winner in two consecutive spins of the roulette wheel.

I am pretty sure the answer is either 4/38 X 4/38 , or 4/38 X 1/38.

 

[chiro]

That is the correct answer, but you have to realize the assumptions that are made to get the correct answer.

The main assumption you are using is independence. Also due the the nature of the experiment, you are doing a duplicate of the first trial which means each trial has the same probability.

Simple definition of probability is P(Event) = Number of events in Event / Number of events in total.

Independence implies that for two events A and B, P(A and B) = P(A) x P(B).

Your P(A) = 4/38 and since B is the same event as A, P(B) = 4/38

Typically when we talk about pure randomness we typically use independence as a way to emphasize randomness.

If however the second spin of the wheel depended on the first, then you would not be able to use the independence relationship and it would get more complicated.

 

[Ivan91]

Yeah, but there is no way the second spin depends on the previous one, unless the roulette is illegally manipulated ;)
So, is 4/38 x 4/38 the correct answer?/

 

[HallsofIvy]

Givem a fair wheel, (4/38)(1/38) is the probability that one of your four numbers came up on the first spin and then the same number came up on the second spin.

(4/38)(4/38) is the probability that one of your four numbers came up on the first spin and one of your four numbers came up on the second spin.

 

[CellCoree]

Your question is correct, the probability of winning with at least one of your numbers in two consecutive spins of the roulette wheel is 4/38 x 4/38. This is because each spin of the roulette wheel is an independent event, so the probability of winning on the first spin is 4/38 and the probability of winning on the second spin is also 4/38. To calculate the probability of both events happening, we multiply the probabilities together. Therefore, the probability of winning with at least one of your numbers in two consecutive spins is 4/38 x 4/38, which is approximately 0.01 or 1%.