Women, math, and the Monty Hall problem

[PureX]

Having 2 choices doesn't mean the odds are 50/50.
50/50 only applies when there's no additional information.

And in this instance, there is no "additional information". There is only a bit of theater that leads some people to think they have some additional information. And it's interesting and fascinating how determined some of those folks are to maintain that illusion.

 

[Revoltingest]

And in this instance, there is no "additional information".

Monty's telling us which door in the unchosen
group is a goat isn't new information?

There is only a bit of theater that leads some people to think they have some additional information.

Correct on both counts!

And it's interesting and fascinating how determined some of those folks are to maintain that illusion.

Oops.....you failed.

 

[Stevicus]

You could pick the fire door, or no doors at all, initially, and still Monty is going to eliminate one door with one goat, and ask you to pick again. So the three door choice scenario is just irrelevant theater that has no bearing on the ACTUAL choice the contestant is given, and the ACTUAL possible outcomes.

The other angle to this is that, while deciding whether to switch doors or to stick with their original choice, the contestant is in a room full of noisy people yelling out trying to influence their choice, while Monty Hall is pressuring them by offering them cash to switch. There's also a time limit in play where the contestant does not have much time to think or consider the odds.

 

[Evangelicalhumanist]

It's only "trinary" in your mind. In actuality it's two doors and two possible outcomes.

You can flip the coin a thousand times and still not come up with 500/500. Mathematics is based on abstract ideals. Reality is based on some degree of chance and complex happenstance.

And there is no third door involved in the choice being presented. There are only two doors to choose from and two possible results (unless Monty eliminates the door with the car, but of course he does not do that).

It doesn't matter because Monty is NOT going to open that door. He is going to open whichever other door has a goat behind it, and then ask you to choose again. So this part of the "game" is not relevant to the odds involving the choice you make. It's just theater.

Which leaves you with a 50/50 chance of picking the door with the car, or the door with the goat. So that "information" is of no use whatever.

You could pick the fire door, or no doors at all, initially, and still Monty is going to eliminate one door with one goat, and ask you to pick again. So the three door choice scenario is just irrelevant theater that has no bearing on the ACTUAL choice the contestant is given, and the ACTUAL possible outcomes.

If you say so....

....and who would know better, after all? Certainly not all those mathematicians --- how could they know nearly as much as you?

 

[Revoltingest]

If you say so....

....and who would know better, after all? Certainly not all those mathematicians --- how could they know nearly as much as you?

@Wirey once gave me a pearl of wisdom that was something like....
"It's always a school janitor who knows the truth...not experts in the field."

 

[Revoltingest]

You could pick the fire door, or no doors at all, initially, and still Monty is going to eliminate one door with one goat, and ask you to pick again. So the three door choice scenario is just irrelevant theater that has no bearing on the ACTUAL choice the contestant is given, and the ACTUAL possible outcomes.

Probability is often difficult to calculate.
It can be simplified with decision trees showing all possibilities.

This diagram shows every possibility for each of 3 doors chosen.
The purple boxes show results of switching the initial choice.
Add up the probabilities of switching doors to see a 2/3 chance of getting a car.

 

[We Never Know]

That's the whole point. the fact that one door is revealed doesn't change the number of doors, does it? Listen, I understand how compelling the 50-50 intuition is. Like I expressed in my opening post, I was snagged by it too.

It doesn't even matter if Monty asked you to switch doors. When he reveals one door and its a goat, your odds just doubled regardless if you switch.

 

[Revoltingest]

It doesn't even matter if Monty asked you to switch doors. When he reveals one door and its a goat, your odds just doubled regardless if you switch.

Wrongo pongo.
See post #106.

 

[icehorse]

If anyone disagrees with the OP, I'd be more than happy to set up a test of 100 tries, let's say for maybe $5 a try?

 

[Wirey]

@Wirey once gave me a pearl of wisdom that was something like....
"It's always a school janitor who knows the truth...not experts in the field."

I thought I told you my school janitor had good drugs, but okay. After all, I was pretty high.

 

[We Never Know]

Wrongo pongo.
See post #106.

Doesn't matter.

You picked a door.

You started off 1/3

Monty gave you another door for free. You then had 2/3

 

[Wirey]

As an aside, this math problem is described at length by the monster masquerading as a protagonist in Mark Haddon's "The Curious Incident of the Dog in the Night-Time".

 

[Revoltingest]

Doesn't matter.

Math is hard, eh.

 

[We Never Know]

Probability is often difficult to calculate.
It can be simplified with decision trees showing all possibilities.

This diagram shows every possibility for each of 3 doors chosen.
The purple boxes show results of switching the initial choice.
Add up the probabilities of switching doors to see a 2/3 chance of getting a car.

This goes back to this post ..

What you have to figure out is... Is Monty trying to get you to switch from your door because its a winner or because its a loser.

 

[icehorse]

Didn't read the whole thread, so sorry if this explanation has already been used. It sometimes helps people understand:

Imagine 52 doors (you can use a deck of cards). After the first guess, Monty opens up all the doors except the guessed door and one other door...

 

[Revoltingest]

This goes back to this post ..

Monty's intentions are irrelevant to the fundamental math.

 

[Revoltingest]

Didn't read the whole thread, so sorry if this explanation has already been used. It sometimes helps people understand:

Imagine 52 doors (you can use a deck of cards). After the first guess, Monty opens up all the doors except the guessed door and one other door...

That needs re-phrasing to be clear.

 

[We Never Know]

Math is hard, eh.

Not at all. Starting off you automatically get two of three doors because Monty will always show a goat to start.
That's what the odds doubling is based on. You start off it 33.3%, Monty shows you a goat and your odds double to 66.6%.

 

[Revoltingest]

Not at all. Starting off you automatically get two of three doors because Monty will always show a goat to start.
That's what the odds doubling is based on. You start off it 33.3%, Monty shows you a goat and your odds double to 66.6%.

The odds only double if the choice is switched.

 

[icehorse]

That needs re-phrasing to be clear.

Two points:

1 - I'd be happy to try this experiment with you, 100 times for $5 a go?

2 - Go back to the OP. After you make your guess, Monty opens up 50 doors to show 50 goats... So, initially you had a 1/52 chance of being correct. You make your guess. Switching back to using a deck of cards... at this moment, you had your pile of one card and there was another pile of 51 cards. Do you agree that until a card is turned over the odds are 51/52 that the bigger pile contains the winning card? Now, Monty turns over 50 of the 51 cards leaving 1 from the bigger pile...