[spamtrap1888]

On May 19, 7:54*am, Carey Carlan wrote:
spamtrap1888 wrote in news:88df2861-f695-449b-
:



Let's look at the case of the ignorant host.

There are three possibilities at the start of the game. The
probability of each is 1/3

_1 2 3_
aCGG
bGCG
cGGC

Let us say door 1 represents the contestant's pick. The host can pick
either door 2 or door 3
Case a: Host picks Door 2. Result: Goat. Contestant switches to Door
3, loses.
..............Host picks Door 3 *Result Goat. Contestant switches to
Door 2, loses.
Case b: Host picks Door 2. Result Car. Contestant loses
..............Host picks Door 3. Result Goat. Contestant switches to
Door 2, wins
Case c: Host picks Door 2. Result Goat. Contestant switches to Door 3,
wins
..............Host picks Door 3 *Result Car. Contestant loses.

Of the six possible scenarios, the contestant loses four times. If the
contestant does not switch after the ignorant host opens a door, the
contestant loses four times. If we discard the times the host opens a
door with a car behind it, the contestant wins two out of four times
when he switches, and two out of four times when he doesn't switch.
Therefore, switching picks has no effect on the odds when the host
randomly opens one of the other doors.

Then go back to the original where the host knows where the car is and
the contestant switches.

Case a: Host picks Door 2. Result: Goat. Contestant switches to Door 3,
loses.
..............Host picks Door 3 *Result Goat. Contestant switches to
Door 2, loses.
Case b: Host picks Door 3. Result Goat. Contestant switches to Door 2,
wins
Case c: Host picks Door 2. Result Goat. Contestant switches to Door 3,
wins

Or the contestant doesn't switch.

Case a: Host picks Door 2. Result: Goat. Contestant keeps Door 1, wins.
..............Host picks Door 3 *Result Goat. Contestant keeps Door 1,
wins.
Case b: Host picks Door 3. Result Goat. Contestant keeps Door 1, loses
Case c: Host picks Door 2. Result Goat. Contestant keeps Door 1, loses

After the Host opens the door the odds are even. *Makes no difference if
the contestant changes doors or not. *This is the same as there only
being two doors.

The original claim was that the odds remained 1 in 3 even after the Host
opened the door. *I still don't see it.

Without switching, the contestant has a 1/3 chance of winning:
Case a: Contestant picked door with car. Host can open either door,
his choice, to reveal goat.
Case b: Contestant picked door with goat. Host must open Door 3 to
reveal goat.
Case c: Contestant picked door with goat. Host must open Door 2 to
reveal goat.

With switching, the contestant now has a 2/3 chance of winning:
Case a: Host can open either door, his choice. Contestant switches to
unopened door, loses.
Case b: Host opens Door 3, contestant switches to Door 2, wins.
Case c: Host opens Door 2, contestant switches to Door 3, wins.