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Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Do any of you have any noteworthy experiences where knowledge of math helped you in an unusual way?
https://en.wikipedia.org/wiki/Monty_Hall_problem
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Get Those Brain Cells Working: The Monty Hall Problem
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(Score: 1) by Mike on Friday July 29 2016, @04:05PM
Actually I think the solution is slightly different.
First, what I'll call the "real politic" solution. If the common wisdom is to switch to the other unopened door, then your choice should be based on whether you think they want to give a car away or not (i.e. have they given a car away lately, how frequently do they seem to give a car away etc...). Basically, try to figure how they are gaming the system.
But assuming total random chance, I think the stats are more along the lines of figure what are the odds that the other two doors are both empty: 2/3 * 2/3 = 4/9. The chance that one of the doors has a car is 5/9. Your choice then becomes 4/9 for the first choice and 5/9 for the unopened choice. Close to 50/50, but it's still slightly better odds to go for the other door.
If you've done some research on the game, though, what I called the 'real politic" solution would probably give you better odds than that.
(Score: 1) by toddestan on Friday July 29 2016, @10:50PM
The "real politic" solution is only in play in the host has the option of revealing the goat and allowing you to switch. In that case, your odds of winning when switching can be as low as 0% (the host only offers to switch when he knows you've picked the car) to 100% (the host is out to help you and only offers you the switch if you've picked one of the goats). But in the problem as presented, the host's hands are tied. He must always offer the option to switch and must always open a door that contains a goat. In that case, the odds of winning the car by switching is 2/3. Which is simple if you think about it, as the chances of initially picking the door with the car is 1/3, and that doesn't change when the host reveals a goat behind one of the other doors, which means that if you stay you have the same 1/3 odds, and therefore switching gives you 2/3 odds*.
"Real politic" might come in handy if you've figured out the placement of the car is not random, or there's a pattern to which goat the host reveals when he has a choice. But that information will only help you so you should still have at least 2/3 odds of winning the car.