The Monty Hall Problem: maths/probability mind bender

[Halibut]

Consider the problem if there are lots of doors- say 100 (Total_Doors).

 

There are 100 doors, behind 1 door is the prize, the remainder have goats.

 

So pick a door. You have a 1 in 100 chance of picking the prize. That is; a very good chance of picking a goat:- remember you have probably got a goat.

 

The host knows what's behind every door,

 

The rules say

a) if the chosen door contains the prize the host must open 98 doors (Total_Doors - 2 ) containing goats, leaving the chosen door and a goat door

b) if the chosen door contains a goat the host must open 98 (Total_Doors - 2 ) doors containing goats, leaving the chosen (goat) door and the prize door

 

You are now given the opportunity to stick or switch ( remember when you started off you have probably picked a goat ). So you switch, and

there is a very good chance of winning the prize.

 

The above rules apply for any number of doors, in the Monty Hall example the total number of doors is 3, so the host can only open 1 door.

 

That's by far the best explanation I've ever come across - thankyou!

[Brentner]

Consider the problem if there are lots of doors- say 100 (Total_Doors).

 

There are 100 doors, behind 1 door is the prize, the remainder have goats.

 

So pick a door. You have a 1 in 100 chance of picking the prize. That is; a very good chance of picking a goat:- remember you have probably got a goat.

 

The host knows what's behind every door,

 

The rules say

a) if the chosen door contains the prize the host must open 98 doors (Total_Doors - 2 ) containing goats, leaving the chosen door and a goat door

b) if the chosen door contains a goat the host must open 98 (Total_Doors - 2 ) doors containing goats, leaving the chosen (goat) door and the prize door

 

You are now given the opportunity to stick or switch ( remember when you started off you have probably picked a goat ). So you switch, and

there is a very good chance of winning the prize.

 

The above rules apply for any number of doors, in the Monty Hall example the total number of doors is 3, so the host can only open 1 door.

 

Whoa... Thank you! A very good explanation indeed. Took me a while, but I get it now.

[Jeffrey Shaw]

I like this type of mindbender, even though I guessed wrong.

But I'm puzzled by the counterposing of goats and cars. In what context are they ever plausible alternative choices?

[altus]

I like this type of mindbender, even though I guessed wrong.

But I'm puzzled by the counterposing of goats and cars. In what context are they ever plausible alternative choices?

 

They are not meant to be vaguely equivalent prizes. There's be no jeopardy in making the wrong choice if a contestant would be happy to win either prize.

[Jeffrey Shaw]

And look at the car: nifty product placement by Cadillac!