Question

Consider the Monty Hall exercise in your textbook: “On the game show Let’s Make a Deal, hosted by Monty Hall, a contestant chooses one of three closed doors, two of which have a goat behind them and one of which has a car. Monty, who knows where the car is, then opens one of the two remaining doors. The door he opens always has a goat behind it (he never reveals the car!). If he has a choice, then he picks a door at random with equal probabilities. Monty then offers the contestant the option of switching to the other unopened door. If the contestant’s goal is to get the car, should she switch doors?” Now, consider a variation of this situation, where instead of three doors, you are initially presented with four doors, three with goats and one with a car. Everything else stays the same (you pick one initially, and the host opens only one of the other doors with a goat). What is the probability of winning if you decide not to switch? Present your result in the normal probability form, the decimal form (for instance, 0.5 for a 50%, or ½ chance), with two decimal places.

          Consider the Monty Hall exercise in your textbook:

“On the game show Let’s Make a Deal, hosted by Monty Hall, a contestant chooses one of three closed doors, two of which have a goat behind them and one of which has a car. Monty, who knows where the car is, then opens one of the two remaining doors. The door he opens always has a goat behind it (he never reveals the car!). If he has a choice, then he picks a door at random with equal probabilities. Monty then offers the contestant the option of switching to the other unopened door. If the contestant’s goal is to get the car, should she switch doors?”

Now, consider a variation of this situation, where instead of three doors, you are initially presented with four doors, three with goats and one with a car. Everything else stays the same (you pick one initially, and the host opens only one of the other doors with a goat).

What is the probability of winning if you decide not to switch? Present your result in the normal probability form, the decimal form (for instance, 0.5 for a 50%, or ½ chance), with two decimal places.

Consider the Monty Hall exercise in your textbook:

“On the game show Let’s Make a Deal, hosted by Monty Hall, a contestant chooses one of three closed doors, two of which have a goat behind them and one of which has a car. Monty, who knows where the car is, then opens one of the two remaining doors. The door he opens always has a goat behind it (he never reveals the car!). If he has a choice, then he picks a door at random with equal probabilities. Monty then offers the contestant the option of switching to the other unopened door. If the contestant’s goal is to get the car, should she switch doors?”

Now, consider a variation of this situation, where instead of three doors, you are initially presented with four doors, three with goats and one with a car. Everything else stays the same (you pick one initially, and the host opens only one of the other doors with a goat).

What is the probability of winning if you decide not to switch? Present your result in the normal probability form, the decimal form (for instance, 0.5 for a 50%, or ½ chance), with two decimal places.

Added by Rhonda C.

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