Suppose you will be shown three prizes in order. You know absolutely nothing about how valuable the prizes might be; only after viewing all three can you determine which one you like best. You are shown the prizes in order and are allowed to select one. However, there is no going back. You must select a prize immediately after seeing it, before seeing any subsequent prize.
a. Your sole objective is to obtain the best of the three prizes. (Second best does not count.) A random selection provides a one-third chance of getting the best prize. Find a strategy that provides a greater chance.
b. What if there are a large number of prizes (say, 10, 50, or 100)? Describe in general terms the kind of strategy that would maximize your chances of obtaining the best prize.