A few days ago I shared my shaken faith in Robert Leroy Ripley, the New York City sports cartoonist who, in 1918, at the age of 25 found himself stuck for something to draw. According to the keepers of his legend, he “dug into his files where he kept notes on all sorts of unusual sports achievements” and did a little collection of oddities, including a Canadian who (believe it or not) ran the 100-yard dash in 14 seconds — backwards. One thing led to another, including the opening in Chicago in 1933 of his “Odditorium,” stocked with odd items he’d collected from around the world, which, believe it or not, 2.5 million visitors came within one year to see. (Times were simpler then — and no TV.)
Anyway, what shook me was this item: “Mrs. E.H. Bisch’s 3 children of Santa Rosa, Calif., all have the same birthday! The odds against three children in the same family being born on the same date are 28,000,000 to 1.”
As I pointed out a few days ago, the odds of this are in fact not at all 28,000,000 to 1. “The first kid could have been born any day [I wrote] — the odds of that are 100%. So what are the odds each of the next two would be born the same day, wherein lies the remarkable occurrence? The answer is 1 in 133,225 (365×365), if you don’t nag me about leap years. Not common, to be sure. Not likely. But not 1 in 28 million, either.”
Well, leave it to my wonderful readership to run with this and point a ton of things I missed.
In the first place, thanks to those of you, like Monty Goolsby, who pointed out that even with his faulty logic his math was wrong. Ripley was apparently multiplying 365x365x365 to get his number, but this was back in the days before pop-up calculators. Pressing Ctrl-N in my trusty old DOS version of Managing Your Money and raising 365-1/4 to the third power, I get 48,727,112. So he didn’t mean 28 million to 1, he meant 48 million.
But that’s just math. It’s the logical nuances you noticed that were more interesting.
Writes John: “Not to nag the point too much further, but the odds of the 3 children with the same birthday could be even less than 1:(365 x 365). If the parents are inclined to have such an occurrence, they could plan things out 9 months ahead and further increase the odds. From what I remember of my wife’s OB/GYN telling her, the normal gestation period for humans is 40 weeks +/- 2 weeks, so then the odds could really be as low as 1:(28 x 28) = 784 to 1. That’s even less than the Pick 4 lotteries!
From Glen: “I’m surprised that you didn’t point out that a child’s birthday is hardly a matter of random chance. I know a family with five children, all born within about two weeks of each other. The father’s birthday is about three months later — or nine months earlier, depending on how you count.” I.e., we know what HE gets for his birthday.
Eric Pollack says he “would be shocked to learn that they didn’t actually TRY for the same birthday with the third” child, which makes a lot of sense, too. And, he adds, “the same assumptions of randomness corrupt market evaluations. Look for reasons behind and beyond the numbers, and you’ll have a better shot at making predictions.”
Finally, there’s this from Mark Brady, which can make you twenty bucks: “I enjoyed the Ripley’s story because in our family we had three pairs of birthdays, three days apart. My fiance and myself, my mother and her mother, and my sister and her husband. Of course we had a lot of family members to choose from, as well as the range of days apart. Which leads me to ask: In a room of 20 people, how often will two people have the same birthday? Most people guess 20/365 or about 5% of the time. In reality, the probability is above 99% because you are comparing each person with every other person in the room.”
I was aware of that one, as you may have been, too. But most people find it astounding. So it’s not a bad way to win $20 in a bet.
Tomorrow: Back to the S.E.C.
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