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Yes, very cool, but the probabilities are way off on this. This is significantly more likely than 1/500,000 You have to factor in: 1) This same article would have been written if it was 19 girls, rather than boys. That is, "heads" or "tails" is not critical, which cuts the odds in half. 2) This same article would have been written if, at any point, a streak of 19 had appeared. This hospital has been "flipping this coin" for many years 3) This same article would have been written if this had occurred in any other regional hospital. There are several coins being flipped. 4) OK, I'm guessing no one else cares but I hope this helps.
Using the boy/girl ratio mentioned in the article, I put it at 3.288 chances in a million, or 1/312500. Of course, any series of 19 boys and girls has the same probability. 3 boys, then 4 girls, then 2 boys, then 5 girls, then 3 boys, then 2 girls has exactly the same probability as a string of 19 boys or a string of 19 girls. The hospital staff just doesn't notice it as much.
littlepeople All good points. You also have to consider that the possibility starts over with each birth, given that it is a continuous sequence. Thus, similar events would be likely to occur once for every 2^18 births, which occurs every few years in Minnesota. Also, if you have multiple different sequences, such as for different subsets of the same set of births, (same hospital, same birth room, etc.), such events could occur on a proportional basis. What *would* be highly unlikely is if such events never occurred.
If you do the probability "correctly" (because it's all in how you want to look at it), you will find that once every 9-10 years this occurs in MN. "this" being a streak of exactly 19 same gender births. As littlepeople suggests it's about the streak probability. The calculation is, 60,000 total births/year in MN, 150 hospitals in MN = 400 births/hospital/year. The streak probability of exactly 19 same gender births out of 400 is 0.073%. So, that's 0.073%*150 = 11% chance every year. So, once every 9 years or so.
I'm glad others have noticed the faulty logic here. The author of this article needs to read up on the gambler's fallacy. Each birth is an independent event, just like each flip of a coin. The probability of 19 boys and zero girls is exactly the same as any other combination of boys and girls.
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