Richard Gonzalez found my triplot.R function and enhanced it by adding a graphical user interface. By the use of sliders, one can change the beta parameters a and b, the data values s and f, and see the effect of the changes on the triplot (prior, likelihood, and posterior) and the predictive distribution.

Here are a couple of illustrations.

In the first example, the prior is beta(3, 7) and one observes 6 successes

In the second example, the beta(6, 2) prior is in conflict with the data (s=6, f=14) and the observed number of successes is in the tail of the predictive distribution.