Hi, Bustino. 1. Yes, it was 1963. Racing was off from 5th January until 8th March. I believe 46-47 was bitterly cold as well, but I wasn't born until '47 , so I don't remember much about it! When Mill House slaughtered the classy Fortria in mid March, the thaw had come and the testing ground suited him. Thinking back, what a wonderful horse Fortria was- three miles+ wasn't his distance, but he would still have won the Gold Cup in many years.I remember his winning the Mackeson under 12st 7lbs. Fred Winter tried to make all on the bottom weight, School For Gamble, but Fortria joined him over the last and murdered him up the hill. 2.This is also from the 62-63 season. Mill House lost just once from his five races- he was beaten by Stan Mellor who "pounced" on King's Nephew in a tactical affair for The Cottage Rake Chase at Kempton . Amazing when you think how far Mill House beat him when second to Arkle in '64.
Ok this is a famous question and caused some degree of fuss a few years back. You are on a quiz show and the quizmaster shows you 3 doors behind one of which is a Mercedes Saloon. Behind the other two are dinky car models. You are asked to pick one door and if you are right you get the car. You choose the middle door. The quizmaster (who knows where the car is) then opens the left hand door and there's a model car behind it. He then asks you do want to stick with the middle door? The question is: should you change to the Right Hand Door or stay with your first choice?
Good morning, Bustino. An interesting poser! Why does the quizmaster open the left hand door- instead of just opening the middle door to reveal whether the contestant was right or wrong? Or is the key in the question- " You are asked to pick one door and if you are RIGHT, you get the car?" However,I'd have to say that "you" means anyone and not just the contestant. Therefore, the logic is ....the quizmaster picked the left hand door. "If you are right ( of the door you pick), you get the car." Therefore the "right" of the door you pick is the middle door. Answer..stay with your first choice. PS. I accept that if "you are right" could simply mean the right hand door, but by opening the left hand door, the quizmaster negated that choice- and you have to be "right" of the one you pick.
You're good at these sort of things aren't you Tam. Don't know if you are right but I wouldn't have even thought of that. I think I'll stick with the one in the middle too, following your logic.
Your chance of being right with your middle door choice is 1 in 3. Your chance of being wrong is 2 in 3. Just because the quizmaster opens a door and reveals the Mercedes wasn’t behind that door doesn’t contain the car doesn’t improve your odds. You should therefore change your choice. If that’s not satisfactory for you it is probably because there are just 3 doors. What happens if there are a 100. You choose a door and same conditions the quizmaster knows where the car is and opens 98 doors where the car isn’t. He then asks you if you’ll change to the other door. Your original chance was 1 in 100. Under these conditions you’d be barmy not to change. 3 or 100 it actually doesn’t make a difference, you increase your chances by changing.
Bustino, fair enough. I realise now that it's a type of "statistical" solution(I now think I've heard a similar one years ago)- as opposed to one where the clue is in the wording. Good question, though.
I must have explained that well and you must have a really good feel for it because there were plenty of Maths professors in the US who went into print and embarassed themselves. The problem was first proposed in the New York Times and when the columnist gave the solution without the explanation she received an avalanche of derision from them. She then explained it and they all had rather red faces.
I'm not a maths professor so no chance of me embarassing myself but ....................... this is a bit of a trick question isn't it because they are actually 2 independent situations. In the first situation you have to choose 1 from 3, in the second you have to choose 1 from 2. The 2 choices are completely independent of each other. When the first door has been opened and you are asked whether you want to change your mind, you are actually now answering a completely different question. If you stay where you are you have a 1 in 2 chance. If you change your mind you have a 1 in 2 chance. So either way you are improving from your original 1 in 3 chance.
I agree with Oddy. I don't see how moving improves your chances. If you eliminate the 3rd door which has been opened, then you have a 1 in 2 choice between the door you had previously chosen and the other door. Surely it doesn't matter which you then choose? i.e. Mathematically the chance is 50:50 whichever door you choose . . . Unless I'm missing something, which is possible . . .
So what about the 100 doors example? Remember the quizmaster knows where the car is as well. In the 3 door example your chance of being right will not increase from 1 in 3. Sure sometimes you'll be right but statistically you'll be wrong 2 out of 3 times. It's not a trick. If you want to increase your chances of being right you change. The two choices are not independent...you chose 1 door and you have a 0.33 probability of being right. Just because another door is opened dooesn't increase your probability. If you think that explain how you wouldn't change with the 100 door example.
Bustino, I thought someone might put forward Oddy's/Zen's argument about choosing 1 from 2 ie. 50%, but I know statisticians go along with your reasoning. On a slightly different tack, I once read somewhere that statisticians do not accept it's 50/50 when you shout "head or tails?" They say human error gives you slightly less than 50% chance of being right. Most people won't accept that.
With the 100 door case you are initially required to pick 1 door from 100 - therefore you have a 1 in 100 chance of hitting the right one. When one is opened, you are then in a new situation where you are required to pick one door from 99. If you stick with your original choice you have a 1 in 99 chance of being correct. If you change to another door, you also have a 1 in 99 chance of being correct. The fact that you now have a better chance than before (i.e. 1 in 99 as opposed to 1 in 100) is due to the fact that one door has been taken out of the equation. Whether you stick with your original choice or change, your chances of being correct have increased from 1 in 100 to 1 in 99. Don't forget statisticians also claimed that 8 out of 10 cats preferred whiskers
"Don't forget statisticians also claimed that 8 out of 10 cats preferred whiskers" Nice one Oddy! If you've ever visited Pedigree Petfoods at Melton Mowbray, you'd know that none of them "prefer" Whiskers! It's just that they're brainwashed into eating all the sh-t that comes in tins!
Tam did you ever see the episode of Red Dwarf where they ran out of food and Lister ended up eating dog food from a tin? I'm sure they put something tasty in there for him during the shoot but it looked absolutely revolting
No, I'ver never watched Red Dwarf, although I believe it's excellent. Have you seen the film District 9- where Aliens are living in a "concentration- type camp" in Sowjeto. It's really funny and Whiskers is their favourite food. The locals call the aliens "prawns" and I'd highly recommend the film; it's stupidly hilarious.
Still agree with Oddy. Whichever way you look at it you have two different choices to make: Choice 1: You can choose any of the three doors. You therefore have a 33.33% chance of choosing correctly. The quizmaster opens one of the other doors showing the car is not behind that one. Choice 2: You can now choose between the two remaining doors. Although your 'choice' is to stay or change, this is exactly the same as having a choice between the two remaining doors, ie middle and right. In the example quoted, you have chosen the middle door in choice 1, and the quizmaster has opened the left hand door. This leaves the middle door and the right hand door remaining. You have the choice to change (ie pick the right hand door) or to stick (ie pick the middle door). I fail to see how your original choice impacts upon this decision. If you substitute the word right for change and middle for stick, then your original choice is irrelevant. You then have a 50:50 chance of being correct, regardless of which door you choose. The exact same explanation applies for 100 doors, 1million doors, or whatever. I suppose the thing I don't agree with is that the two choices are not independent. I think they are.
The 100 example is that the quizmaster opens 98 doors, leaving your choice and one other door. Your chance of being right was 1 in a 100. Do you honestly think your chance of being right is now 1 in 2? I can tell you it isn't. If you did the same exercise 100 times you might be right 1 time to stay with your original choice, you might be lucky and get 2 by a fluke but 90 odd times you'd be wrong. So what if there are originally 90 doors, or 80 or 3, it's all the same logic. You improve your chances by changing. Don't worry millions would agree with you.
Ah OK, I see what you mean about the 100 example. That does make more sense. Perhaps a better way of explaining it is you can choose one of the three doors (33.33%), leaving two of the doors (66.66%). The fact that the quizmaster eliminates one of the doors (one without the car) means that you in effect have 'two' doors on your side by changing. If that makes any sense at all . . .
