2. Game Show Host Problem: There used to be a TV show called The Price is Right. In the game, a contestant selects 1 of 3 doors. Behind one of the doors is the grand prize. The contestant selects a door and then after some back and forth the game show hosts says, "let me show you what is behind one of the doors you did not select". He shows the contestant what is behind one of the two doors not chosen and then asks, "Now the grand prize is behind one of the two doors. Do you want to keep the door you have or switch to the door you did not choose"? Some people say keep the door you have because the probability that you have the grand prize is now - i.e. 1 out of the 2 doors remaining (since the host showed you what was behind one door already). Simulate this game and determine if this is a good strategy or not