P

#### pna

For anyone interested in the maths and not critisizing others because they dont agree...

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The odds on the Monty Hall scenario are 50-50.

Axiom: (from the website listed in this post) It is important to note here that Monty would NOT open the door that concealed the car.

Proof:

Three doors - A, B and C. Let us suppose the Car is behind A, and goats behind B and C.

Scenario 1 (you choose the car first time)

Let us suppose the contestant chooses A. Monty Hall opens B (or C) and asks if you want to swap A for C (or B). You still dont know what is behind any door and you have a straight choice between keeping A or swapping for C - a car is behind one, a goat behind the other but you dont know. 50-50.

Scenario 2 (you choose a goat first time)

Let us suppose the contestant chooses B (or C). Monty Hall opens C (or B) and asks if you want to swap B (or C) for A. You dont know what is behind B (or C) and A, so again its a straight choice between a car and a goat. 50-50.

Confusion:

The website poses the question:

"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?"

But then subtly changes the problem:

"Omitting one phrase in the statement of this problem changes the answer completely and this might explain why many people have the wrong intuition about the solution. If the host (Monty Hall) does not know where the car is behind the other two doors, then the answer to the question is "IT DOESN'T MATTER IF THE CONTESTANT SWITCHES."

However the initial statement, as quoted on the same website says "Monty would NOT open the door that concealed the car."

**But he can only do this if he knows where the car is!**

So there is an inconsistency - who knows what the actual question is that the website author thinks they are answering (with such apparent authority) but its not the initial question.