Probably the most confusing blog in the world

A: I’ve been reading about probability this week.

B:Are you sure?

A: Yes. There’s a very interesting problem concerning 2 goats and a car.

B: Shoot.

A: OK. Stay with me for this – it’s a bit tricky.

B: OK.

A: On a tv show contestants can win either a goat or a car.

B: Why?

A: Because……. I don’t know – perhaps they’re Capricorns?

B: If they were Pisces?

A: It would be 2 fish and a car I guess.

B: You digress.

A: I do. There are 3 doors on this t.v. show and behind each door is either a goat or a car.

B: 2 goats. 1 car.

A: Correct. And before you ask – you can’t hear or smell the goats.

B: Or the car?

A: Or the car.

B: Go on.

A: The host asks the contestant to choose a door. The winning contestant chooses a door.

B: Door number 1, 2 or 3.

A: If you like.

B: I like. Oh by the way does the host know where the car and goats are?

A: Yes. This is important.

B: Glad I asked.

A: OK. So the contestant chooses 1, 2 or 3. Then comes the intriguing part.

B: What – the door is opened.

A: No. The door isn’t opened

B: What happens?

A: Well, the host opens one of the doors not choosen to reveal a goat.

B: Whilst the contestant…

A: Whilst the contestant still has the door they’ve already choosen. They may even stand by it – if they like.

B: Intriguing.

A: That’s not the intriguing part. The next bit is.

B: Pray tell.

A: Well the host then asks the contestant if they want to change their mind.

B: And?

A: And invariably the contestant says ‘no’. How crazy is that?

B: Not that crazy.

A: It’s ridiculous.

B: Why?

A: Well – if the contestant changes their mind they have twice the chance of winning the car, of course.

B: Of course (pause). I see it now?

A: No you don’t. But it is true though. Trust me. It’s maths.

B: And this proves?

A: That it’s often difficult to adapt – change your perspective – change your TOR.

B: Tor? Mountain? Get to the top of the tor and change your point of view?

A: Terms of Reference.

B: I knew that. But seriously, talk me through the goat thing.

A: Well – it’s to do with where you are.

B: (A long drawn out) OK…..

A: At the start you choose a door and have a 1 in 3 chance of getting the car. Right?

B: Check.

A: When you’re asked if you’d like to change your mind the TOR are different.

B: (A longer drawn out) O.K…………

A: Look at it from the point of view of the prize behind the door that the contestant hasn’t chosen and hasn’t been opened.

B: I can do that.

A: If you’re a car – you won’t be opened – obviously.

B: Obviously. Because …?

A: Because you’re a car and the host wouldn’t give the game away.

B: Ah ha.

A: So therefore you have a 2 in 3 chance of being a car…

B: Because there are only 3 options for the doors that are not the contestant’s choice….

A: Which are a) car/goat, b) goat/car or c) goat/goat.

A: Exactly.

B: So by eliminating the goat as an option in all three

A: You are left with options …a) car b) car or c) goat.

B: So as a contestant if you worked this out you know…

A: You would change…. QED.

B: Quite Easily Done?

A: Quod Erat Demonstrandum.