Hazmat wrote:
According to Wikipedia, hypothyroidism occurs in "between three and ten percent of adults, with incidence higher in women and the elderly". The odds of a coach and both of his star runners all suffering from this condition is thousands to one against.
Math help for Hazmat:
1. Calculating the odds. The venerable Wiki suggests that hypothyroidism occurs between 3% and 10% of adults. This is wide range (which indicates inaccuracy), but accepting these results, the possibility that any random combination of coach and athlete having this same condition is either 0.9% (9/1000) or 10% (100/1000) or, taking the average provided by the venerable Wiki, 3% (30/1000).
2. Using the odds, part 1. Since there are thousands of coach-athlete combinations, it is actually not unlikely that Salazar-Rupp have the same condition. It only seems unlikely to you because you aren't looking at the other thousands of pairs.
3. Using the odds, part 2, survivorship bias. Since Salazar has this condition, he isn't included in the "odds" of Rupp having this condition. This is the coin flip dilemma. The odds of flipping heads 8 times in a row are very low (about 0.4%), but if you flip 7 heads in a row the odds that the next flip is heads is still 50%. So if Salazar has this condition, the odds that Rupp has this condition are the same as any other adult (which is, apparently, 3-10%) and these odds are not decreased by Salazar already having this condition.
You are very welcome,
-Adam Smith (deceased)