Brain teaser

[handsome]

"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?"

* Behind each of three doors is either a goat or a car (two goats, one car).
* The player picks one of the three doors. The contents are not revealed.
* The game host knows what is behind each door.
* The game host must open one of the remaining doors and must make the offer to switch.
* The game host will always open a door with a goat.
* That is, if the player picks a door with a goat, the game host picks the other door with a goat.
* And if the player picks the door with a car, the game host randomly picks either of the two doors with a goat.
* The host offers the player the chance to either claim what is behind the originally-chosen door, or to switch, claiming what is behind the one remaining door.

Do the player's odds of getting the car increase by switching?

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