Game Show
Here is the setup. You are on an old game show where
there are three curtains and a prize behind exactly one of them. You choose
the curtain that you think the prize is behind. At this point, the
game show host will point to one of the other two curtains and tell you that
he knows the prize is not behind this curtain. You now have the option
to change your guess to the remaining curtain the prize could be behind or
to keep your initial guess. What strategy should you choose in order
to maximize your probability of winning, and what is this probability. In
other words, is it better to change your answer or to keep your initial guess?