Re:The Time Everyone “Corrected” the World’s Smartest Woman ...
by galaxyLogic on Tuesday May 11, 2021 @02:16AM
(#27114801)
I came up with a slightly different reasoning why you should switch: When the host is about to open a door there are 2 possibilities, he can either choose between 2 goats, OR he can choose between a car and a goat.
In more than 50% of the cases the host encounters the situation where he must choose between a car and and goat. Why because in > 50% of the cases the user's initial choice does NOT have car behind it, so the host must choose between a goat and a car in > 50% of the cases.
And of course he chooses the goat. So in > 50% of the cases the remaining door will have the car behind it,
So by switching, you have > 50% chance of winning the car. Is this the correct answer? It would seem to me your chance to win if you switch is 1/2 x 2/3. Is this correct?
What is counter-intuitive is why the action by the host should give us any information about which door has the car. And it does not do so always. It only gives us information in 2/3rds of the cases. If the host chooses between two goats that should not give us any information at all should it? But that is good enough for us since we play the odds, and switching seems to increase our odds.
But, now I have my doubts. This kind of probabilistic reasoning would seem to apply only if we repeat the experiment many times. But no contestant gets to play this game more than once. Probability theory does not tell us anything about what happens in a single experiment. So is it rational for the player to think they should switch if they can play this game only once?
How much should they be willing to pay for the option of being able to switch the door, if they know they can only play this game once?
In more than 50% of the cases the host encounters the situation where he must choose between a car and and goat. Why because in > 50% of the cases the user's initial choice does NOT have car behind it, so the host must choose between a goat and a car in > 50% of the cases.
And of course he chooses the goat. So in > 50% of the cases the remaining door will have the car behind it,
So by switching, you have > 50% chance of winning the car. Is this the correct answer? It would seem to me your chance to win if you switch is 1/2 x 2/3. Is this correct?
What is counter-intuitive is why the action by the host should give us any information about which door has the car. And it does not do so always. It only gives us information in 2/3rds of the cases. If the host chooses between two goats that should not give us any information at all should it? But that is good enough for us since we play the odds, and switching seems to increase our odds.
But, now I have my doubts. This kind of probabilistic reasoning would seem to apply only if we repeat the experiment many times. But no contestant gets to play this game more than once. Probability theory does not tell us anything about what happens in a single experiment. So is it rational for the player to think they should switch if they can play this game only once?
How much should they be willing to pay for the option of being able to switch the door, if they know they can only play this game once?