Ok. This is a new theme i have been considering writing about. It should be fun but what i need are evveryday problems for which information is uncertain and a decision must be made. Here is a very simple and oft discussed example. Suppose that you are on the show Let's Make a Deal. The scenario is as follows. You are shown three curtains and told behind the curtains are three prizes. One of the prizes is valuable the other two are generally not valuable. You are asked to pick a curtain. At this point you have a 1/3 chance of having selected the curtain with the prize behind it. You are then shown that behind one of the curtains that you did not choose is one of the crummy prizes. You are then asked whether you would like to stick with the curtain you initially chose or switch and choose the other remaining curtain.
If you stick with your original choice you still have a 1/3 chance of winning. On teh other hand, the prize had a 2/3 chance of being in one of teh other two curtains. This remains true even after you have been shown that a crummy prize was behind one of those two. As a result, the remaining curtain of the two still has a 2/3 chance of having the prize. Thus switching doubles your chances of winning. Neato!