By the final round of the quiz, the contestants have been whittled down to a single contender. This contestant is presented with three closed doors, behind one of which is the week's Star Prize.
She chooses one of the three doors, but this door isn't opened straight away. Obviously, the contestant may or may not have chosen the correct door, but either way there are TWO other doors and only one star prize. So the presenter (who knows where the prize is) is free to open one of those other two doors, safe in the knowledge that the prize ISN'T behind it. He does this.
The contestant now knows that the prize is behind one of two doors. It's either the one she originally chose, or else the only other unopened door.
On average, should she stick with her original choice, or change her mind and switch to the other unopened door? Or doesn't it make any difference, on average, which one she chooses?