### What are the odds of that!

So, last year at the AP Reading, we played putput golf at one of those kitschy golf centers in Daytona Beach. Somehow, I managed to trap the ball on a cylindrical totem pole on a steep incline on the 8

^{th}hole. No! It is not a testament to my skill since I very smartly brought up the rear in our six-some. However, how does one manage to trap the ball on so impossible a spot? I had been thinking about the occurrence (probably far more than it merited), because when I came back to the hotel I wrote about it… Months later as I am clearing up the random thoughts that I am given to confiding to my computer and I have come across this one. I am not sure how much clarity in this train of thought was induced by the half dozen G&Ts I consumed before I put fingers to keyboard…

According to Bayes' theorem, the probability of event A (trapping the ball on the totem) given event B (finding a totem on a green) depends not only on the relationship between A and B (i.e., finding a totem on a green) but on the absolute probability (trapping the ball on the totem) of A not concerning B (i.e., trapping the ball on the totem in general), and the absolute probability of B not concerning A (i.e. the probability of finding a totem on a green). Thus, if 95% of the putts sucked so much as to trap the balls on the totem, this could be due to 5% false positives, 5% false negatives (good putts), or a random mix of false positives and false negatives. Using Bayes' theorem allows one to calculate the exact probability of trapping the ball on the totem, given a consistently bad putt for each case, because the probability of B (finding a totem on a green) will be different for each of these cases. It is worth noting that if 5% of bad putts result in a trapped ball, then the probability that an individual traps the ball on the totem is rather small, since the probability of totem actually showing up on a putting green is closer to 1%. The probability of a totem on a green is then five times more likely than the probability of trapping the ball on the totem itself. Answering your question, it is entirely possible!

Clearly, I have far too much time on my hands….!

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