Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from four hidden windows. Behind each is one of the following: $150,000, $200,000, $1 million, or a "stopper". Before beginning, the contestant is offered $100,000 to stop. Mathematically speaking, should the contestant take the $100,000?

Question

Consider a state lottery that has a weekly television show.  On this show, a contestant receives the opportunity to win $1 million.  The contestant picks from four hidden windows.  Behind each is one of the following: $150,000, $200,000, $1 million, or a "stopper".  Before beginning, the contestant is offered $100,000 to stop.  Mathematically speaking, should the contestant take the $100,000?