Plotting it out forces the reader to try to visually calculate the integral. Wikipedia gives a nice treatment of how to get a numerical answer to "What is the probability that this coin is fair:" http://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair...

I actually tried including an analytic solution as well, but it took up a lot of space and seemed like clutter. I figured most people would prefer the graphical solutions anyways.

Thanks for the link, I should include that inside the post somewhere. EDIT: Done.