Pointing Out the Obvious wrote:
concernedBQer wrote:4. Odds of bib 2161 being missed by random chance at these
three locations: (25/200)x(2/200)x(7/200) = 1 in 22857. Put another way,
that makes it a 99.996% chance he didn't run through those locations.
You do not seem to understand statistics. This is a very common failing among the human species.
Please note:
A) "Given that someone ran through those three locations what are the odds that they would fail to show up in any picture taken at said locations?"
and
B) "Given that someone failed to show up in any pictures at those three locations what are the odds that they actually ran through all of them?"
are two fundamentally different questions.
Re. (B), you have to consider the additional piece of information that there's a photo of him crossing the finish line. So that leaves two possibilities, he either went through all 3 locations and was missed by random chance (question A), or he only went through 0,1, or 2 of the 3 locations, plus the finish line. The second possibility results in automatic disqualification. So to prove cheating, all you need to show that the scenario in question A has a very low odds of occurring.
If we assume that the three locations are independent Bernouilli trials (e.g., nobody told the photographers to explicity not photograph him), with p_1 = 1/200, p_2 = 25/200, p_3=7/200, where the p's are the prob. of being missed by the photographers, then multiplying the probs. is appropriate, giving 1 in 45714 odds of being missed by chance at all three locations.
By the way, you could get a considerably better probability estimate (and lower the odds even more) by increasing the photo analysis to the top 500 (or all) runners, and using all the photo locations on the course except the finish (there's at least 6 including a sequence 200 yards from the start line - no sign of Rossi there either). If you conservatively assume 50% of the top 200 runners were photographed at those other locations, the odds drop to 1 in 365712. The real question is, what odds would the VIA race director accept for a DQ?