A famous problem in probability comes from the game show “Let’s Make a Deal.” In it, a...

A famous problem in probability comes from the game show “Let’s Make a Deal.” In it, a contestant is shown three doors. Behind one door is a new car, and behind the other doors, there is nothing. The contestant is asked to pick one of the three doors. The host then opens up one of the two that was not chosen which always reveals that there is nothing behind that opened door. The contestant is then asked if he or she would like to change their chosen door to the other unopened one.

A) Should he/she? Explain why or why not. (Expresses opinion about whether the contestant should change his/her decision, and supports that opinion through sound application of the concepts of probability)

B) Can you think of another example where someone's intuition about probability may lead them down the wrong path?

Expert Solution

A) This is famous Monty hall problem

He/she should change his door, because

B) other example could be

You are a legally blind person looking for a disabled parking space. They come as the Os in X,X,O,X,X,O,X,X,O,… as repeated infinitely. Every third space is a disabled space. You pull into one but can’t see the markings below your car on the road. Immediately after you, The Game Show Host, Peter, pulls in right next to you - either on the left or right. Because you know that he isn’t disabled you also know that he will never park in a disabled spot. Peter has revealed the true probabilistic landscape of the parking lot. Understanding the repetition of the disabled parking spaces you restart the engine of your car and buffer out a move of one space in the opposite direction of where Peter has parked right next to you (and this is you switching your selection). Believe it or not you have probably seen this before, in real life.

orchestra answered 1 year ago

John is watching an old game show rerun on television called Let’s Make a Deal in...

John is watching an old game show rerun on television called Let’s Make a Deal in which the contestant chooses a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $130, and behind the other is a round-the-world trip worth $8,500. The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected...

John is watching an old game show on rerun television called Let’s Make a Deal in...

John is watching an old game show on rerun television called Let’s Make a Deal in which you have to choose a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $ 150, and behind the other is a round-the-world trip worth $7,200. The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is...

The Monty Hall problem is a famous problem loosely based on the game show Let's Make...

The Monty Hall problem is a famous problem loosely based on the game show Let's Make a Deal. You are a contestant on the game show. There are 3 doors in front of you. Behind one door is a prize, and behind the other two doors are goats. Assume the door with the prize is picked uniformly at random from the three doors. First, you pick a door. Then, Monty Hall will open one of the other two doors that...

Imagine you are on a the game show "Let's Make a Deal" and are given the...

Imagine you are on a the game show "Let's Make a Deal" and are given the opportunity to select one closed door of three, behind one of which there is a prize. The other two doors hide goats or some other such non-prize, or nothing at all. Once you have made your selection, Monty Hall will open one of the remaining doors, revealing that it does not contain the prize. He then asks you if you would like to switch...

Suppose it’s the 1970’s and you’re on the show Let’s Make a Deal. The host, Monty...

Suppose it’s the 1970’s and you’re on the show Let’s Make a Deal. The host, Monty Hall, would offer the “Big Deal” to a contestant at the end. In exchange for their current winnings, they would be able to choose one of three doors. Behind one of the doors is a very big prize that you would want (We will call this the “winning door”), and behind the other two doors is something you would not want. Whichever door you...

Let’s see what happens when Let’s Make a Deal is played with four doors. A prize...

Let’s see what happens when Let’s Make a Deal is played with four doors. A prize is hidden behind one of the four doors. Then the contestant picks a door. Next, the host opens an unpicked door that has no prize behind it. The contestant is allowed to stick with their original door or to switch to one of the two unopened, unpicked doors. The contestant wins if their final choice is the door hiding the prize. Let’s make the...

2a) Suppose you are playing “Let’s Make a Deal”, the “prize” is worth $10,000, and a...

2a) Suppose you are playing “Let’s Make a Deal”, the “prize” is worth $10,000, and a goat is worth nothing. Further suppose that the initial pick of a door is not part of the game (since it’s random anyway). You’ve always picked door A initially before the game has begun. The game starts as nature randomly determines where the prize is (1/3 chance for any of the three doors); then Monty Hall selects one of doors B or C that...

2c) Suppose you are playing “Let’s Make a Deal”, the “prize” is worth $10,000, and a...

2c) Suppose you are playing “Let’s Make a Deal”, the “prize” is worth $10,000, and a goat is worth nothing. Further suppose that the initial pick of a door is not part of the game (since it’s random anyway). You’ve always picked door A initially before the game has begun. The game starts as nature randomly determines where the prize is (1/3 chance for any of the three doors); then Monty Hall selects one of doors B or C that...

2b) Suppose you are playing “Let’s Make a Deal”, the “prize” is worth $10,000, and a...

2b) Suppose you are playing “Let’s Make a Deal”, the “prize” is worth $10,000, and a goat is worth nothing. Further suppose that the initial pick of a door is not part of the game (since it’s random anyway). You’ve always picked door A initially before the game has begun. The game starts as nature randomly determines where the prize is (1/3 chance for any of the three doors); then Monty Hall selects one of doors B or C that...

The Monty Hall problem is named for its similarity to the Let's Make a Deal television...

The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, someone who knows wh at's behind...

Question