Probability

Bayes' Puzzle Powers

A while ago, the popular data journalism site 538 posted a challenging probability puzzle: On the table in front of you are two coins. They look and feel identical, but you know one of them has been doctored. The fair coin comes up heads half the time while the doctored coin comes up heads 60 percent of the time. How many flips — you must flip both coins at once, one with each hand — would you need to give yourself a 95 percent chance of correctly identifying the doctored coin?

Empirical Bayes to Estimate NBA Treys

All sports statistics are imperfect measures of a player’s performance. At best, they show relative differences in how well athletes shoot, steal, and rebound. At worst, they are marred by rule changes and outside factors that either exaggerate or handicap certain subgroups of players. The NBA’s measure for three-point accuracy is one of worst kinds of the latter. Between 1995 and 1997, the NBA changed the distance of the three-point line, biasing all future comparisons between generations of players.

Deranged X-Mas - a Gift Exchange Puzzle

While planning a holiday gift exchange this week, my wife casually challenged me with a sort of tricky probability puzzle: Sara and I were talking today and realized that we were off by one on the rotation because last year we went sledding instead of buying gifts. It should actually be: * Sara gives to Jonny * Jimmy gives to Thurop * Amy gives to Lisa * Jonny gives to Sara * Thurop gives to Jimmy * Lisa gives to Amy