When I was at uni, this formula was proven by two lots of mathematical induction (the second of which I can't remember), however, by using the principle of inclusion/exclusion, which is essentially what James did here, the formula just drops out.
This logic seems correct but it is not. The key is what Monty is allowed to do and each choice he makes carries the same weight. Monty can open 4 doors. He can 1. open Door 2 leaving Door 3 with a Goat 2. open Door 3 leaving Door 2 with a Goat 3. Forced into opening Door 2 leaving Door 3 with a Car 4. Forced into Opening Door 3 leaving Door 2 with a Car Doing some basic maths that leaves either of the remaining Doors with a 50% change of being a Goat or a 50% chance of being a Car. The key thing here is that whatever Monty chooses it also increases the chances of what is behind your original choice. Your original choice has increased to 40% of having a car because of Montys action and the remaining exposed door has a 60% chance of having the car because of Montys action.
"Doing some basic maths that leaves either of the remaining Doors with a 50% change of being a Goat or a 50% chance of being a Car." "Your original choice has increased to 40% of having a car because of Montys action and the remaining exposed door has a 60% chance of having the car because of Montys action."
@@klaus7443 Read what I said. The remaining Doors are Doors 2 and 3 and either one remains we dont know which one. The remaining Doors are NOT the one you chose. That Door has already been locked in at 33%.
Consider an open problem e.g. "There are no odd perfect numbers". If I understood correctly, this statement can be translated to a map which admits a legal 3 colouring if and only if the statement is true. Since the map is finite, I can test in finite time whether or not the map admits a legal 3 colouring. This means that if the statement is true, there is a proof of it and if it is false, there is a proof that it is false; in other words it cannot be undecidable. This is puzzling: how can this be correct? I think that I am making a logical error but I cannot see it: can somebody help me here?
It's simple but not efficient. He said that the map might be humongous (as in have a larger number of countries than the number of atoms in the observable universe).
