Ph.ds Vs a college dropout

sambarvada wrote:http://www.marilynvossavant.com/articles/gameshow.html


===> Read the responses by so many math and stat professors.

How come they got it wrong?

sambarvada wrote:http://www.marilynvossavant.com/articles/gameshow.html


===> Read the responses by so many math and stat professors.

How come they got it wrong?

carvaka on old CH wrote:The correct answer to the game show puzzle
is counter-intuitive. This is because of two reasons:

1. human psychology / behavior
2. conditional probability


1. Human psychology / behavior: The host is a person. When we think of
people making decisions, we intuitively look for their motives and then
deduce the decisions they might make from their motives. We assume that
the host is trying to "win" the game, or to be precise, that the host is
trying to prevent the player from winning the car. If the host is
indeed doing this, switching does not pay. If you initially picked an
empty door, the host can open the door with the car, and you immediately
lose. If you initially picked the car, the host will open an empty door
and give you the option to switch. In this instance, you should NOT
switch. So the dominant strategy (the strategy that wins more often than
others) is to NOT switch. However, vos Savant and others who responded
to FF's question here made the assumption that the host is NOT trying to
actively prevent the player from winning. Under this assumption, it
DOES make sense to switch.



2. Conditional probability: Imagine a person who just tuned into the
program after the empty door has been opened by the host. If this person
now picks one of the two remaining doors, the probability that he picks
the car is indeed 1/2. He has no prior information about what happened.
So why is the probability that the player will win if he switches 2/3?
The key thing here is the information that the player has. The host knows where the car is. The host uses
that knowledge to decide which door to open (he always opens an empty
door.) Indirectly, the player has the information that the door that the
host will open will CERTAINLY be empty. Imagine a different scenario.
If the host was completely unaware of where the car is. He opens one of
the two doors not picked by the player. Some times it has a car; at
other times it doesn't (the probability that there is a car behind the
door the host opens: 1/3.) Once the door has been opened thusly, if
there happens to be no car behind that door, the probability the car is
behind each of the remaining doors is simply 1/2. Because the host did
NOT use fore-knowledge of where the car is to decide which door to open,
the odds are even. However, in the game show puzzle, the host does use
his knowledge of where the car is. Hence the changed odds.



Counter-intuitive results occur in situations where the simplified rules
(aka heuristics) we use for everyday decision-making are not
sophisticated enough to deal with a nuanced problem. The game show
puzzle is one such nuanced problem.

sambarvada wrote:
I think you should let it go instead of beating up people like Seva. IMO there is virtue in letting the other guy save his face than to obliterate and humiliate someone.

sambarvada wrote: think you should let it go instead of beating up people like Seva. IMO there is virtue in letting the other guy save his face than to obliterate and humiliate someone.