2006/9/10, Björn Helgason <[EMAIL PROTECTED]>:
> The probability of new toss of a coin is not dependent
> on the previous tosses
There is no coin, in the original context.
> You now have a 50/50 chance of choosing your door or the other
You have 100% chance of choosing the door you choose.
But which door has the car behind it?
> The probability is even anything else is just plain silly
The probability of what? Of a coin toss landing a specific
way? Sure.
For that matter, if you flip a coin to decide whether you switch
or stay, then your probability of picking a car is 50%.
But there are three doors, and the probability of a car appearing
behind any one of the doors is not 50%, it's roughly 33%. So if
you do not switch, you have, roughly, a 33% chance of picking the
right door.
Furthermore, if you do switch, and the car was behind the door you
originally picked, you lose. So you have at least a 33% chance of
losing if you switch.
However, if the car was not behind the door you originally picked,
a goat was behind that door, and there are only two goats.
Here's how I like to simulate this:
NB. door numbers
doors=: 1+?~3
NB. door indices
car=: ?3
mine =: 0
monty=: {.(?~3)-.car,mine
To find door numbers (assuming you're interested in that), use:
car { door
mine { door
monty { door
As for whether or not I win:
If I don't switch, I win if mine=car, and lose otherwise.
If I do switch, I lose if mine=car, and win otherwise.
Why do I win if I switch and mine~:car? Because when mine~:car I
picked a goat, monty picked the other goat, and there are only two
goats.
In other words, regardless of how large n is, and regardless of
how many times you run the following, its result is always true:
n=: 1e6
mine=: n#0
cars=: ?n#3
montys=: {."1 (?~n#3) -."1 cars,.mine
*./ (0 = cars) +. cars = (?~n#3) -."1 montys,.mine
--
Raul
2006/9/2, Roger Hui <[EMAIL PROTECTED]>:
> The object of the game is to win a car.
>
> Two goats and a car are hidden behind 3 doors, one
> item per door. You choose a door. The gamemaster
> (Monty Hall), who knows what's behind the doors,
> opens one of the other doors, revealing a goat, and
> offers you the opportunity to change your choice of
> doors. Your chosen door is then opened and you get
> what is behind.
>
> Should you stick or switch?
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