# The Monty Hall Dilemma and Probability

Consider roulette, a popular game that can be found in most casinos around the world. In the game, a small ball is rolled within a spinning wheel that contains differently colored (red, black, and green) and numbered markers (0, 00, and 1–36). Half of the numbers, 1–36, are red and the other half are black. In European versions of the game, there is a 0 that is green, and in American versions, there is a 0 and a 00 that are green. Before the wheel is spun, the players will place their bets on either a color, number, or a combination of both, and each choice presents a different set of odds. For example, placing a bet on an “even” number or on “red” will pay out 1:1. A player can choose to bet on a single number too, with a payout of 35:1. A player could also choose a set of numbers, such as 1–12 for a payout of 2:1. If a player bet \$100 for each of these examples and won, the winnings would be \$100, \$3,500, and \$200 respectively.

With these payouts, it may seem that the odds are as even for the player as they are the casinos, almost as if it was a fair game. But, someone with an understanding of probability will realize that the casinos have a slight advantage that—if played out time and time again—will always favor the casino and create profits for them. If there were only 36 numbers, the risks would be evenly distributed for most picks, but you must also include the 0 and the 00 into the equation. The odds for the player of a 1:1 bet are not 50/50—they are 47.4% for the player and 52.6% for the casinos for an American style roulette table.

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In this Discussion, you will examine a well-known statistical problem that represents the concepts of probability and the benefits of how this concept can influence decision making.

Post a 150- to 225-word (2- to 3-paragraph) explanation of how the Monty Hall dilemma can be applied to management decisions. In your explanation, address the following:

• Explain your thoughts on the Monty Hall dilemma, including what the correct choice is and why, any challenges you may have faced in accepting the answer, and how your opinion may have changed while reviewing this week’s Learning Resources. For example, do you still have a difficult time accepting the results?
• Managers often make decisions about problems that have similar amounts of uncertainty as the Monty Hall dilemma. What can this exercise teach them about making decisions under uncertainty, and what would be an example of this lesson in practice in a business environment?
• To support your response, be sure to reference at least

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