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?

How many times do you want to run the experiment? (10000>=R>=3)

How many doors do you want there to be? (>=3)

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...
109LosesWins
94LosesWins
22WinsLoses
81LosesWins
29LosesWins
52LosesWins
13LosesWins
54LosesWins
66WinsLoses
1010WinsLoses
98LosesWins
48LosesWins
36LosesWins
95LosesWins
1010WinsLoses
910LosesWins
98LosesWins
31LosesWins
910LosesWins
11WinsLoses
85LosesWins
29LosesWins
86LosesWins
23LosesWins
11WinsLoses
310LosesWins
96LosesWins
72LosesWins
25LosesWins
61LosesWins
54LosesWins
104LosesWins
23LosesWins
41LosesWins
25LosesWins
110LosesWins
102LosesWins
97LosesWins
81LosesWins
109LosesWins
22WinsLoses
810LosesWins
85LosesWins
19LosesWins
106LosesWins
104LosesWins
1010WinsLoses
71LosesWins
21LosesWins
14LosesWins
Sum292263842
Mean5.84005.26000.16000.8400
© Severecci 2001 — 2005