Can you answer this veridical paradox?

[The Doctor]

I have read this before in a book by John Douglas of the FBI. As another poster has identified, the OP is referring to the Monty Hall problem. Once you have established behind one door is a goat, you take it back to the start. You had 3 possibilities:
If you had Goat 1 originally, if you stick you keep Goat 1. You know the other door is Goat 2 now. If you twist, you get a Ferrari.
If you had the other goat it is the same. Stick, you keep Goat 2. You know behind the other door is Goat 1. Twist you get a Ferrari.
If you have a Ferrari, then stick you keep it. Twist you will get either Goat 1 or 2.

There were 3 scenarios, and in two of them twisting gets the star prize. If there was an even 33.3% chance before you were given a door, then there is a 66.6% chance that switching will benefit you.

Good explanation, and using it as a basis I am going to have another go at an explanation to see if I can further help any of the doubters!

SWITCHING
If you choose the Ferrari first time (1 in 3 chance) then you end up with a goat if you switch
If you choose a goat first time (2 in 3 chance) then you end up with a Ferrari if you switch
So switching results in a Ferrari in 2 out of 3 scenarios

STICKING
If you choose the Ferrari (1 in 3 chance) and stick you win the ferrari
If you choose a goat (2 in 3 chance) and stick you win a goat
So sticking results in a Ferrari in 1 out of 3 scenarios

Thus... you are twice as likely to win the Ferrari if you switch than if you stick.

The gutting thing though is that if you DO (unknowingly) pick the Ferrari at the outset and then switch (as you should) then you lose the Ferrari and feel terrible.

 

[GreenThing]

I have read this before in a book by John Douglas of the FBI. As another poster has identified, the OP is referring to the Monty Hall problem. Once you have established behind one door is a goat, you take it back to the start. You had 3 possibilities:
If you had Goat 1 originally, if you stick you keep Goat 1. You know the other door is Goat 2 now. If you twist, you get a Ferrari.
If you had the other goat it is the same. Stick, you keep Goat 2. You know behind the other door is Goat 1. Twist you get a Ferrari.
If you have a Ferrari, then stick you keep it. Twist you will get either Goat 1 or 2.

There were 3 scenarios, and in two of them twisting gets the star prize. If there was an even 33.3% chance before you were given a door, then there is a 66.6% chance that switching will benefit you.

Good explanation, and using it as a basis I am going to have another go at an explanation to see if I can further help any of the doubters!

SWITCHING
If you choose the Ferrari first time (1 in 3 chance) then you end up with a goat if you switch
If you choose a goat first time (2 in 3 chance) then you end up with a Ferrari if you switch
So switching results in a Ferrari in 2 out of 3 scenarios

STICKING
If you choose the Ferrari (1 in 3 chance) and stick you win the ferrari
If you choose a goat (2 in 3 chance) and stick you win a goat
So sticking results in a Ferrari in 1 out of 3 scenarios

Thus... you are twice as likely to win the Ferrari if you switch than if you stick.

The gutting thing though is that if you DO (unknowingly) pick the Ferrari at the outset and then switch (as you should) then you lose the Ferrari and feel terrible.

I was wrong, with these explanations I see it now.

 

[Pogleswoody]

Sorry; makes no sense at all to me and I got grade E Maths O level in 1966!!!

The Ferrari is behind the middle door, a goat riding a donkey on each side. I am shown the goat riding a donkey on the left. Do I want to switch to the door on the right? I am asked. No, says I , cos I think there is a goat riding a donkey on the right and a Ferrari in the middle. I stick and ... get the Ferrari! :thumbs:
How can changing to the door on the right increase my chance of winning a Ferrari when it is behind the middle door?? !!
It can't!! :facepalm:

 

[GreenThing]

Sorry; makes no sense at all to me and I got grade E Maths O level in 1966!!!

The Ferrari is behind the middle door, a goat riding a donkey on each side. I am shown the goat riding a donkey on the left. Do I want to switch to the door on the right? I am asked. No, says I , cos I think there is a goat riding a donkey on the right and a Ferrari in the middle. I stick and ... get the Ferrari! :thumbs:
How can changing to the door on the right increase my chance of winning a Ferrari when it is behind the middle door?? !!
It can't!! :facepalm:

When you made your choice, it was more likely that you chose a donkey. Your choice of a likely donkey doesn’t change when you are shown another donkey, all that changes is that it removes the chance of trading a donkey for another donkey.

 

[The Doctor]

Sorry; makes no sense at all to me and I got grade E Maths O level in 1966!!!

The Ferrari is behind the middle door, a goat riding a donkey on each side. I am shown the goat riding a donkey on the left. Do I want to switch to the door on the right? I am asked. No, says I , cos I think there is a goat riding a donkey on the right and a Ferrari in the middle. I stick and ... get the Ferrari! :thumbs:
How can changing to the door on the right increase my chance of winning a Ferrari when it is behind the middle door?? !!
It can't!! :facepalm:

Well in the scenario where you HAVE guessed the Ferrari door at the start then, yes, you should not switch, but if you haven’t guessed right initially then you SHOULD switch (as my previous post demonstrates). But you don’t KNOW whether you have guessed right or wrong at the start and because you are twice as likely to have guessed wrong than to have guessed right the best decision is to switch. Obviously this still doesn’t guarantee that you win the Ferrari but it definitely increases you chances of doing so.

 

[Bryan Tregunna]

... and putting it another way: if three of you each select a different card and you all stick, one of you will get a car.

But if you all switch, two of you will get a car!

 

[AdelaideGreen]

Sorry; makes no sense at all to me and I got grade E Maths O level in 1966!!!

The Ferrari is behind the middle door, a goat riding a donkey on each side. I am shown the goat riding a donkey on the left. Do I want to switch to the door on the right? I am asked. No, says I , cos I think there is a goat riding a donkey on the right and a Ferrari in the middle. I stick and ... get the Ferrari! :thumbs:
How can changing to the door on the right increase my chance of winning a Ferrari when it is behind the middle door?? !!
It can't!! :facepalm:

Poggles. Are you sure that you aren't too carried away with the idea of goat riding donkeys.

The isolation of Covid-19 can do strange things to you.

 

[Pogleswoody]

Sorry; makes no sense at all to me and I got grade E Maths O level in 1966!!!

The Ferrari is behind the middle door, a goat riding a donkey on each side. I am shown the goat riding a donkey on the left. Do I want to switch to the door on the right? I am asked. No, says I , cos I think there is a goat riding a donkey on the right and a Ferrari in the middle. I stick and ... get the Ferrari! :thumbs:
How can changing to the door on the right increase my chance of winning a Ferrari when it is behind the middle door?? !!
It can't!! :facepalm:

Poggles. Are you sure that you aren't too carried away with the idea of goat riding donkeys.

The isolation of Covid-19 can do strange things to you.

Bliddy Nanny state!!