User talk:Martin Hogbin/Sandbox2

A decision tree on the MHP

=We start with the Whitaker/vos Savant statement= And we assume the normal game rules, that the host must always open an unchosen door to reveal a goat and must always offer the swap. We want to win the car.

We use only information given in the problem statement
Plus minimal real world knowledge. We know what a car, door, and goat are.

We use the above symmetries implicitly
The simple solutions are fine.

We use the above symmetries explicitly
The simple solutions, with explicit mention of the observed symmetries are fine.

We do not notice a symmetry with respect to the doors and a symmetry with respect to the goats
We must use conditional probability, starting with all possibilities allowed under the game rules and then condition on the door originally chosen, the door opened by the host, and the goat revealed by the host.

We use the above symmetries implicitly
The simple solutions are fine.

We use the above symmetries explicitly
The simple solutions, with explicit mention of the observed symmetries are fine.

We do not notice a symmetry with respect to the doors and a symmetry with respect to the goats
We must use conditional probability, starting with all possibilities allowed under the game rules and then condition on the door originally chosen, the door opened by the host, and the goat revealed by the host.

We use the above symmetries implicitly
The simple solutions are fine.

We use the above symmetries explicitly
The simple solutions, with explicit mention of the observed symmetries are fine.

We do not notice a symmetry with respect to the doors and a symmetry with respect to the goats
We must use conditional probability, starting with all possibilities allowed under the game rules and then condition on the door originally chosen, the door opened by the host, and the goat revealed by the host.

We use the above symmetries implicitly
The simple solutions are fine.

We use the above symmetries explicitly
The simple solutions, with explicit mention of the observed symmetries are fine.

We do not notice a symmetry with respect to the doors and a symmetry with respect to the goats
We must use conditional probability, starting with all possibilities allowed under the game rules and then condition on the door originally chosen, the door opened by the host, and the goat revealed by the host.

We are realist/frequentists who make no assumptions about the unknown distributions
The problem is insoluble.

We use our real-world knowledge about game shows
In a modern TV game show the regulations in most countries would require the car to be initially placed randomly, the player to be given a free choice of door, and the door opened by the host to to chosen randomly (when he has a choice) independently of the goat behind it.

We are Bayesians and therefore take all unknown distributions of probability to be uniform
There are now no significant unknown distributions. We take them all to be uniform.

We use the above symmetries implicitly
The simple solutions are fine.

We use the above symmetries explicitly
The simple solutions, with explicit mention of the observed symmetries are fine.

We do not notice a symmetry with respect to the doors and a symmetry with respect to the goats
We must use conditional probability, starting with all possibilities allowed under the game rules and then condition on the door originally chosen, the door opened by the host, and the goat revealed by the host. =We do not start with the Whitaker/vos Savant statement= Your problem - your solution!