Cue PH brainiacs - logic puzzle!
Discussion
Einion Yrth said:
Come on its been five minutes,,,whats the answer
You select a door - you have 1/3 probability of being correct. call this set A.
There is a 2/3 probability that the car is behind one of the doors, call this set B
the host opens one of the two doors that you did not select, to reveal a goat. Set B now consists of one closed door, and one goat, but there is still a 2/3 probability that set B contains the car.
Therefore if you change your choice from set A (1/3 probability) to set B (2/3 probability) you double your chances of winning.
Wrong - in the first choice, there ia a 1/3rd chance of being on the car. Once a door has opened to show a goat, the chances of being on the car are no longer 1/3, they are 1/2.
jap-car said:Why have the probabilities changed? Answer they haven't and I am correct - follow the link I posted for a more intuitive explanation and a simulation program which demonstrates the principle.
Come on its been five minutes,,,whats the answer
You select a door - you have 1/3 probability of being correct. call this set A.
There is a 2/3 probability that the car is behind one of the doors, call this set B
the host opens one of the two doors that you did not select, to reveal a goat. Set B now consists of one closed door, and one goat, but there is still a 2/3 probability that set B contains the car.
Therefore if you change your choice from set A (1/3 probability) to set B (2/3 probability) you double your chances of winning.
Wrong - in the first choice, there ia a 1/3rd chance of being on the car. Once a door has opened to show a goat, the chances of being on the car are no longer 1/3, they are 1/2.
ETA
Of course if the stage hands are free to move the remaining goat and car around while you make your decision, then you would be correct.
>> Edited by Einion Yrth on Friday 9th December 17:25
Einion Yrth said:
Come on its been five minutes,,,whats the answer
You select a door - you have 1/3 probability of being correct. call this set A.
There is a 2/3 probability that the car is behind one of the doors, call this set B
the host opens one of the two doors that you did not select, to reveal a goat. Set B now consists of one closed door, and one goat, but there is still a 2/3 probability that set B contains the car.
Therefore if you change your choice from set A (1/3 probability) to set B (2/3 probability) you double your chances of winning.
Wrong - in the first choice, there ia a 1/3rd chance of being on the car. Once a door has opened to show a goat, the chances of being on the car are no longer 1/3, they are 1/2.
ETA
Of course if the stage hands are free to move the remaining goat and car around while you make your decision, then you would be correct.
>> Edited by Einion Yrth on Friday 9th December 17:25
The probabilities have changed because the information on which you are basing the calculation upon has changed.
Antwerpman said:And therein is the flaw in your reasoning. If the plane were airborne then its intertional frame of reference is indeed the air and to all intents and purposes you can consider it a free motion body. Great - we've just proved that 2+4 = 6. I'm with you all the way there.
For all real purposes you may as well consider the plane flying over the conveyor because the wheels can transmit so little drag on the plane that this is effectively what it will be doing.
But returning to 2+2, whilst the aircraft is on the conveyor belt and is not airborne, its intertial frame of reference is the convoyor belt. Its motive force is immaterial be it driven wheels, propellor, jet power, rocket or porridge-assisted bungee cords. The key fact is that it moves forward by distance d due to its motive power and at the same time the conveyor belt will move by d in the opposite direction, making a net zero forward motion relative to the surrounding air. So there's no airflow.
I'm sorry if you think I'm being abrasive, but I've lost track of the number of times and mumber of different ways I've tried to explain this over the past 2 days.
I'm absolutely certain of my argument, unless physics has changed in the 12 years since I gained a degree in Applied Physics (sorry to have to point that out again, but I want you to know that I'm not just making this up as I go along here)
jap-car said:
The probabilities have changed because the information on which you are basing the calculation upon has changed.
Slightly incorrect - your original choice stood a 1 in 3 chance of being right. This doesn't change.
Thus there is a 2 in 3 chance that your original choice was wrong. Changing your answer to "open both the other 2 doors" therefore gives you a 2 in 3 chance of being right. The fact that one of the wrong choices is automatically removed from "both the other 2" means that the remaining door stands a 2 in 3 chance of being correct.
You have to take the game as a whole (because of the artificial way the odds are stacked by the host ½ way through) to understand it.
gasblaster said:
you should always switch and this is the reason:
3 doors:
door 1 = goat. Stick with door 1 = get a goat. Change = get a car
door 2 = goat. Stick with door 2 = get a goat. Change = get a car
door 3 = car. Stick with door 3 = get a car. Change = get a goat
Note that if you originally chose a goat door (1&2), if you change you get a car because the other goat has already been shown by the host.
So, you stick = 2/3 chance of getting a goat
you change = 2/3 chance of getting a car
>> Edited by gasblaster on Friday 9th December 08:57
reposted for the benefit of those who can't be ar.. don't have the time to read all previous posts
JonRB said:
But returning to 2+2, whilst the aircraft is on the conveyor belt and is not airborne, its intertial frame of reference is the convoyor belt. Its motive force is immaterial be it driven wheels, propellor, jet power, rocket or porridge-assisted bungee cords. The key fact is that it moves forward by distance d due to its motive power and at the same time the conveyor belt will move by d in the opposite direction, making a net zero forward motion relative to the surrounding air. So there's no airflow.
OK I'll bite! As an applied physics graduate, are you comfortable using an accelerating conveyor belt as your inertial frame of reference?
JoolzB said:It's not 50:50 because the host chooses to pick the door you didn't pick, AND the door that isn't a car. If it was random choice then the final stage would be 50:50.
Is there an agreed answer to this as I'm not going to read 6 pages worth. I can't see how it's not 50:50 after the initial goat has had it's cover blown.
moleamol said:
Is there an agreed answer to this as I'm not going to read 6 pages worth. I can't see how it's not 50:50 after the initial goat has had it's cover blown.
Oh right, thought so
BliarOut said:
Is there an agreed answer to this as I'm not going to read 6 pages worth. I can't see how it's not 50:50 after the initial goat has had it's cover blown.
Yes, the goat gets airborne in the end
I'd just listen out for the sound of an engine and the bleeting of a goat and not even bother letting the host do his bit.
moleamol said:
It's not 50:50 because the host chooses to pick the door you didn't pick, AND the door that isn't a car. If it was random choice then the final stage would be 50:50.
The host changing doors wasnt mentioned originally. Even if it is known that the host has the ability to swap the goat and car around it is still a decision he may or may not take, resulting in a 50:50 split. This is assuming the host performs the swap before you confirm your final decision.
JonRB said:
But returning to 2+2, whilst the aircraft is on the conveyor belt and is not airborne, its intertial frame of reference is the convoyor belt. Its motive force is immaterial be it driven wheels, propellor, jet power, rocket or porridge-assisted bungee cords. The key fact is that it moves forward by distance d due to its motive power and at the same time the conveyor belt will move by d in the opposite direction, making a net zero forward motion relative to the surrounding air. So there's no airflow.
I'm sure that is wrong.
The question says the aircraft stays still, and the conveyor belt makes sure it does.
Since the distance the aircraft *would* move forward is not a function of the rotation of it's wheels, but f=ma (minus frictional forces such as wheel drag and air drag), then it's hard to say the conveyor will move the SAME distance as the wheels do.
The belt needs to move at enough speed to generate adequate friction at ANY thrust the aircraft can generate, to offset the forces and equalise them, to generate 0 acceleration.
It's simple really, imagine holding a car on a rolling road that is usually tethered down. You push against it but to stop it moving YOU need to equal a force equal to the frictional drag the tyres are generating to push it forwards...
The point here is that you are unlikely to do that, as the force is huge vs what you can develop, however, it is the same with the aircraft, in *reality* the friction in the wheels may well only equal the thrust generated by the aircraft when the conveyor belt is going at 5000 mph.
The question says the aircraft will not move relative to the conveyor, it doesn't say the aircraft matches the conveyors speed, as the aircraft doesn't have speed for the conveyor to match, the wheels just go as fast as they can to equalise the forces to 0 to keep it still and not accelerate.
I've got A-level physics and I can see to satisfy the question, the forces have to balance, there are only two forces, thrust and drag. To make drag equal thrust we need either super sticky wheels, or a shed load of speed to create the rolling drag in the wheels and energy loss in the bearings through heat!
Either way doesn't matter, but thats what the question is saying. It will stay still in theory. However the conveyor may well drag enough air around the aircraft to make it take off. Depends on the scale of the experiment, but we are asking silly questions now.
Keep It Simple Stupid.
Dave
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