Pregnancy Probabilities

May 2, 2011 at 12:01 pm 1 comment

My twins sons were born on 05/02/07, which is cool because 5 + 2 = 7. Today, they turn 4 years old. Happy birthday, Eli and Alex!

I usually show a picture of them during presentations, and the audience will often ask, “Why are you showing a picture of your sons during a math talk?” Because they’re twins, the response is automatic — “Today we’ll be discussing multiples.”

My wife is pushing 40, and I pushed 40 some time ago, and we do not intend to have any more children. Which reminds me of some sage advice:

Women should never have children after 35. I mean, really… 35 kids is plenty!

Seriously, the traditional age at which a woman is considered to be “high risk” is 35. But the following statement from WebMD, like so many others I’ve read, implies that complications are possible when a woman reaches her 35th birthday that weren’t as likely when she was 34 years, 364 days old:

…complications during pregnancy are more common when women reach age 35.

The truth is, the risk of complications during pregnancy increases with the birth mother’s age, so it would also be true to say that complications during pregnancy are more common when women reach age 26, or 33, or 29, or any other age within the child-bearing years.

My wife and I were lucky. We have friends who, over the course of many years, tried multiple fertility treatments without success. By comparison, we were able to conceive in about 10 months, and we didn’t need the help of modern science. But because success was not immediate, Nadine grew worried. One day, she was particularly sad about it, and I tried to cheer her up. “Don’t worry,” I said. “It’ll happen.”

“But I’m almost 35!” she screamed.

“Yes?” I said, not quite understanding her point.

“What do you mean, yes?” she shouted. “The risk of having a kid with Down syndrome is significantly higher for women over 35.”

I was a little cross to be getting scolded. “That’s true,” I agreed, “compared to a woman who’s 20. But not compared to a woman who’s 34 years, 9 months,” which was Nadine’s age. “If you wanted to significantly reduce the chance of complications, you should have met me a decade earlier.” Needless to say, that comment did not garner a Husband of the Year nomination.

I spent the next several hours collecting data, and later that day, I presented Nadine with the following graph:

Not surprisingly, the likelihood of Down syndrome increases exponentially with the birth mother’s age, and the risk of Down syndrome when the mother is in her mid‑30’s is nearly three times the risk of a mother who is 10 years younger. For a birth mother at age 34, approximately 1 in 617 children are born with Down syndrome; at age 35, approximately 1 in 509 children are born with Down syndrome. So perhaps my statement wasn’t completely accurate. The likelihood of Down syndrome increases nearly 20% when the mother’s age increases from 34 to 35 years.

Nadine and I spent a long time discussing the statistics. I think she felt better when she realized that, even for a mother who is 35, the probability of having a kid with Down syndrome is less than 0.2%.

Speaking of births and twins, the following is a question I’ve posed to various audiences:

In recorded history, what is the greatest number of children born to one woman?

Before I give you the answer, are you sitting down?

Incredibly, the greatest officially recorded number of children born to one woman is 69. She was the first wife* of Feodor Vassilyev (1707‑1782) of Shuya, Russia. (Aren’t you curious why he needed more than one wife?) Unbelievably, 67 of them survived infancy. That would be an amazing mortality rate even today. It’s absolutely astounding for Russia in the middle of the 18th century. What is also unbelievable is that she never gave birth to just one child. Each pregnancy resulted in twins, triplets, or quadruplets. This last fact leads to another question I’ve often posed to audiences:

How many sets of twins, triplets, and quadruplets did she have?

Think about that for a moment, and see if you can find an answer. What you’ll probably realize quickly is that the problem does not have enough information to be solved. So here’s an additional piece of information:

Between 1725 and 1765, she had a total of 27 pregnancies.

Is that enough info to solve the problem?

Actually, it’s not. Even with this additional info, there are still eight possibilities: (19, 1, 7), (18, 3, 6),(17, 5, 5), (16, 7, 4), (15, 9, 3), (14, 11, 2), (13, 13, 1), and (19, 15, 0). So here’s one last piece of data:

She had four times as many sets of twins as quadruplets.

That should do it, and you likely now realize that she gave birth to 16 sets of twins, 7 sets of triplets, and 4 sets of quadruplets. Wow!

* I apologize for not supplying her name. That is not misogyny. Every reference identifies her in relation to her husband but does not give her name.

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1 Comment Add your own

  • 1. Missy  |  May 7, 2011 at 3:03 pm

    Did you factor into your discussion the fact that most babies with Down syndrome are born to women under age 35 because more younger women have babies?

    And that perhaps there could be a flaw in the logic that having a child with Down syndrome = bad? It is certainly different,but not necessarily a universally bad outcome.


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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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