February 03, 2004
Strategies for Event Problems
There are several strategies for event-type problems. Some people try formulas. A better strategy is often a selection from among Venn diagrams, tables, and trees. Other people try raw numbers with no apparent strategy. This latter strategy is not recommended.
We looked at the same information several ways. In each case, the standard strategy is to fill in the entire diagram first and then look to see what the question asks for. Here is the table:
The Venn diagram:
The tree:
Tables accommodate additional rows and columns well, but are not good for more than two dimensions. The tree is good for thinking about sequential processes. The Venn diagram will handle three events, but is no help whatever for four or more events or cases with more than two possible outcomes.
The culimination of our studies of event problems is a quick overview of Bayesian statistics. The mathematics is elegant, and we are all Bayesians to some extent in everyday life, but the problem of picking a prior for unknown parameters is a huge obstacle in "scientific" research. We may have some idea about the prior probability of winning basketball games, but what is the prior probability that Keynes was right about macroeconomics?
