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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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Mr. Jones has devised a gambling system for winning at

Chapter 3, Problem 18STE

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QUESTION:

Problem 18STE

Mr. Jones has devised a gambling system for winning at roulette. When he bets, he bets on red and places a bet only when the 10 previous spins of the roulette have landed on a black number. He reasons that his chance of winning is quite large because the probability of 11 consecutive spins resulting in black is quite small. What do you think of this system?

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QUESTION:

Problem 18STE

Mr. Jones has devised a gambling system for winning at roulette. When he bets, he bets on red and places a bet only when the 10 previous spins of the roulette have landed on a black number. He reasons that his chance of winning is quite large because the probability of 11 consecutive spins resulting in black is quite small. What do you think of this system?

ANSWER:

Step 1 of 2

Our goal is

We need to find what do you think of this system.

Let  denotes a discrete random variable.

Then the outcomes of the  spin with .

Now we assume that both are equally likely and ignore the fact that there is a 0 or a 00 on a Roulette board.

We are assuming independence spins,

So, P( is

.

 

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