![]() (These table mean nothing without first reading the original problem, which can be seen by going to Grand Illusions.) This exercise made things more clear for me, and I hope it does the same for you. I've shown all combinations of car postions, and all combinations of "You pick" / "Monty shows". As you'll see, any one of the examples proves things, but the tremendously counter-intuitive nature of the whole things seems to require TOTAL investigation. |
||
In this first example, the car is
always behind door # 1. |
||
Door # 1 |
Door # 2 |
Door # 3 |
You choose car. |
He shows goat. |
If you switch, you get the goat. |
If you switch, you get the car! |
You choose goat. |
He shows goat. |
If you switch, you get the car! |
He shows goat. |
You choose goat. |
In this second example, the car
is always behind door # 2. |
||
Door # 1 |
Door # 2 |
Door # 3 |
You choose goat. |
If you switch, you get the car! |
He shows goat. |
He shows goat. |
You choose car. |
If you switch, you get the goat. |
He shows goat. |
If you switch, you get the car! |
You choose goat. |
In this third example, the car is
always behind door # 3. |
||
Door # 1 |
Door # 2 |
Door # 3 |
You choose goat. |
He shows goat. |
If you switch, you get the car! |
He shows goat. |
You choose goat. |
If you switch, you get the car! |
He shows goat. |
If you switch, you get the goat. |
You choose car. |