To think that this sum is super simple

[PeerieBreeks]

and can't understand how so many people on Facebook have it so completely wrong (and can justify it to themselves).

Without adding your reasoning, tell me what you think the answer is.

If this question can get over 350 replies I wonder how many the Monty Hall problem would get...

I lost interest in it before the end so I’ll go with the majority vote

Monty Hall? Oh go on then. I love making a fool of myself.

Monty Hall is actually difficult, even for people who (think they) understand probability.

I wouldn't say difficult so much as counter-intuitive. Lois, the problem is:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door at random, and the host, who knows what's behind the doors, opens one of the other doors, which has a goat. He then says to you, "Do you want to stay with your choice or switch?". If you want to win the car, what do you do?

Oh yes! I remember that one... not sure I always remember the solution.

You pick a door, it has a 1/3 probability of being the car
He opens a door he knows is a goat

So now you think, the 2 remaining doors are 50:50... well, no. Your door still has a 1/3 probability of being the car. Just because you now know what 1 of the others had that hasn't changed.

So yes, change your choice... it has a 2/3 probability of being the car!

I have no idea why though!!! I just follow the probability rules and keep my fingers crossed

According to wikipedia, among the people who protested that the published answer to Monty Hall was wrong were 1000 Phds. Nobel prize winning physicists were willing to state in print that the answer was wrong. A famous mathematian said the answer was wrong.

These people all disgreed with the answer, after being told it. They were wrong.

I think that counts as a difficult problem.

Obviously if you take the right approach, it seems simple. The trick is taking the right approach in the first place.

I have no idea why though!!!

ermmmmmm, but you just explained it!

had a door with 1 chance in 3 - switch for the door with 2 chances in 3... common sense.

OK, that's Monty Hall wrapped up. Shall we move on to:

A. Why 0.9 recurring (ie 0.9999999.... ) is equal to 1

or

B. Can a plane on a conveyor belt take off?

Even though I already knew the correct answer, it took me a few minutes to work out again why.

I would state the solution as follows:-

When you make your initial choice, there is a 2/3 probability the car is behind one of the other doors. That is not changed by one of those doors being opened. Given you now know the car is definitely not behind the opened door, there must be a 2/3 probability it is behind the other door you didn't choose.

ermmmmmm, but you just explained it! Nope! As I said, I remembered it, follow the rules as I remember them and hope I remembered it right!

I didn't 'explain' it. I might be able to, in an hour or so, but at the time of typing, I was merely remembering, parrot fashion!

Dad3 or the one about 2 objects never being able to actually collide, cos you can always halve the distance, can't you?

Firesuit, I meant the maths behind the question is simple, but the logic is very counter-intuitive ("there's two doors left so it must be 50-50") which is the joy of the question and why so many people with phds etc get it wrong.

Well he made $90....

Awaits a thrashing haha.

Disclaimer: I know the answer is $20 just in case anybody thought I was being serious.

But, but...my problem with the doors is that, surely, once he opens that goat door, the probabilities ARE different, because the door he opened now has probability of 1, of housing a goat, not 1/3?
So we then have one goat, and one car, behind 2 doors, everything else is known, so why are they not 0.5 probability goat and .5 probability car?
I know I'm wrong, but I don't understand why?!

But it's not 20, surely? He loses 10 then he gains it back so at this stage he has broken even. He then sells a horse for 90 that he bought for 60 - so he has made 30.

20

Xmas - before the host opens a door, the probability that the car is behind one of the two doors you haven't selected is 2/3. When he opens the door, the probability that the car is behind one of the two doors you haven't selected is still 2/3. So it makes sense to switch from your door to the other doors (which means the remaining closed door, because clearly it's not the visible goat that you are picking).

€800, and there's no goat, a unicorn ate it

Dadadad
Can't... comprehend...brain imploding...

Xmas it is because you had a choice of 3 doors when YOU picked.

1 in 3 chance that you picked the right one - so you with a 66% probability (better than even odds) picked the WRONG one. So there is a 66 or 2 out of 3 chance that the door you picked is wrong (that it is one of the other doors, a mere 1 in 3 or 33% probability that you are right..

The host opens one of the other 2 doors - one that YOU DID NOT PICK - a door they KNOW has a goat behind - there is still that 66% probability that the car is behind the other door, and still only 33% that it is behind the door you first picked.

So you have a better chance if you switch.

I have a horse, £20, a car and a unicorn. I'm a happy gal.

It's eighty quid in profit!