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. However, after you see a prize and decline it, 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 and compute the actual chance.

b. What if there is 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. (Do not try to compute an exact answer.)