The trick to understanding this problem is that it is a bit of a "cognitive illusion". The situation is engineered so that at the end you are faced with either a goat or a car; the host knows where everything is and ensures this is the case. The SEQUENCE of events is critical. Imagine you are blindfolded and sit at a table with two blue balls and one red ball. You pick one up in your right hand and then another is placed in your left hand such that you end up with one of each (non-random engineered situation). Think about how likely it is that the red ball is now in your right hand. It is in fact twice as likely that you picked up a blue ball at the start and therefore twice as likely that at the engineered endpoint the red ball has ended up in your left hand.
