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.
A: OK. Stay with me for this – it’s a bit tricky.
A: On a tv show contestants can win either a goat or a car.
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.
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.
A: And invariably the contestant says ‘no’. How crazy is that?
B: Not that crazy.
A: It’s ridiculous.
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?
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.
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.