This is a famous problem, but you may not of heard of it. It could be called the Monte Hall problem after the host to an old US TV show "Let's make a Deal".

A game show contestant is allowed to pick one of three prizes which are each hidden behind a door. Behind one of the doors is a new car, behind the other two are joke prizes like maybe a goat.

After the contestant selects a door at random, Monte shows them that behind one of the doors they didn't select is a goat. He then allows them to trade the one they selected with the remaining hidden prize.

Here is the question: Should the contestant trade doors or keep his own? Does it matter?

Assume here that Monte always offers this choice to the contestants and that he is not doing it because he knows the contestant has chosen the correct door.