Problem: A star prize car is hidden behind one door of several. A contestant is asked to choose one door. Then all the doors are opened apart from the door chosen and one other - the car is behind one of the two shut doors. Is the probability higher of getting the car if you (i) stick with your original choice, (ii) change your mind, or (iii) is it the same probability?
Running the experiment...

There are 10 doors: 1 with a car, 9 with goats.

There is a car behind one door (Door X).

The presenter asks the contestant to choose a door.

The contestant chooses a door (Door Y).

The presenter then opens all but two doors. All the doors the presenter opens
has booby-prizes behind it.

Of the two doors, one has the big prize, one has another booby prize.

The presenter then asks if the contestant wants to stay with his choice, or go
with the other unopened door.

If the contestant had already chosen the grand prize, then changed, the
contestant would loose
it;
if the wrong door was originially chosen, and the contestant changed, the grand
prize would be won.

See the results...

| X
| Y
| Stays with his choice...
| Changes his mind to the other door... |

| 10 | 9 | Loses | Wins |

| 9 | 4 | Loses | Wins |

| 2 | 2 | Wins | Loses |

| 8 | 1 | Loses | Wins |

| 2 | 9 | Loses | Wins |

| 5 | 2 | Loses | Wins |

| 1 | 3 | Loses | Wins |

| 5 | 4 | Loses | Wins |

| 6 | 6 | Wins | Loses |

| 10 | 10 | Wins | Loses |

| 9 | 8 | Loses | Wins |

| 4 | 8 | Loses | Wins |

| 3 | 6 | Loses | Wins |

| 9 | 5 | Loses | Wins |

| 10 | 10 | Wins | Loses |

| 9 | 10 | Loses | Wins |

| 9 | 8 | Loses | Wins |

| 3 | 1 | Loses | Wins |

| 9 | 10 | Loses | Wins |

| 1 | 1 | Wins | Loses |

| 8 | 5 | Loses | Wins |

| 2 | 9 | Loses | Wins |

| 8 | 6 | Loses | Wins |

| 2 | 3 | Loses | Wins |

| 1 | 1 | Wins | Loses |

| 3 | 10 | Loses | Wins |

| 9 | 6 | Loses | Wins |

| 7 | 2 | Loses | Wins |

| 2 | 5 | Loses | Wins |

| 6 | 1 | Loses | Wins |

| 5 | 4 | Loses | Wins |

| 10 | 4 | Loses | Wins |

| 2 | 3 | Loses | Wins |

| 4 | 1 | Loses | Wins |

| 2 | 5 | Loses | Wins |

| 1 | 10 | Loses | Wins |

| 10 | 2 | Loses | Wins |

| 9 | 7 | Loses | Wins |

| 8 | 1 | Loses | Wins |

| 10 | 9 | Loses | Wins |

| 2 | 2 | Wins | Loses |

| 8 | 10 | Loses | Wins |

| 8 | 5 | Loses | Wins |

| 1 | 9 | Loses | Wins |

| 10 | 6 | Loses | Wins |

| 10 | 4 | Loses | Wins |

| 10 | 10 | Wins | Loses |

| 7 | 1 | Loses | Wins |

| 2 | 1 | Loses | Wins |

| 1 | 4 | Loses | Wins |

Sum | 292 | 263 | 8 | 42 |

Mean | 5.8400 | 5.2600 | 0.1600 | 0.8400 |