Fun Probability problem

[Mathew]

What would you think if I stated it like this...

Original Selection:

1. The player originally picked goat 1.
2. The player originally picked goat 2.
3. The player originally picked the car.

Chances of originally selecting the car: 1 in 3.

Correct...

Second Selection:[list=1][*]The player originally picked goat 1. The door with goat 2 is revealed. The remaining door has the car.

Correct

[*]The player originally picked goat 2. The door with goat 1 is revealed. The remaining door has the car.

Correct

• The player originally picked the car. The door with goat 1 is revealed. The remaining door has goat 2.
• The player originally picked the car. The door with goat 2 is revealed. The remaining door has goat 1.

Chances of switching and selecting the car: 2 in 4 (1 in 2)

Nope - there is only 1 car behind the doors not two....

Just because there are four permutations of what can occur doesn't mean you have four choices. It really doesn't matter if you eliminate goat 1 or goat 2 when you have picked the car. If you switch, you will lose either way....



Make this any easier to understand ?