Monty's Dilemma: The Three Door Problem

Description of the problem

In a certain game show, a contestant is presented with three doors. Behind one of the doors is an expensive prize, behind the others are junk (or goats). The contestant is asked to choose a door. The game show host, Monty, then opens one of the other doors to reveal a junky gift behind it. The contestant is then asked if she/he would like to stick with the original door or switch to the remaining door.

The contestant chooses "Door 2". Monty opens Door 3 to reveal a "GOAT". Monty knows which door has the prize and always opens one that has a GOAT behind it. The dilemma is this. Should the contestant
  1. Stick with Door 2?
  2. Switch to Door 1?
  3. Does it matter, i.e., could you flip a coin to decide?