In response to the first pediatric specialist interview I conducted about this mystery, I received two insightful, intelligent, and delightful comments from a reader named “V”. She agreed to share her math skills with us on a broader scale by allowing me to post her work here. As someone who can barely add, I am intrigued by V’s work. And as someone who wants to embrace all possibilities in this sordid tale, I welcome this wonderful way of analyzing the data. Take it away, V.:
One question that has come up several times, in one form or another, has been: what are the odds? I thought it might be interesting to look at various independent data points that we seem to have in Sarah’s story, and assign odds to them, and then apply a little math, in order to determine how likely her story actually is. This is going to be chock full of assumptions and I’m sure the rest of you will have plenty to contribute to make the math better.
Data point/assumption 1: Trig is a Down syndrome baby. As many have noted, an older woman is much more likely than a younger woman to have a DS baby. On the other hand, a younger woman is much more likely to produce a baby. 80% of all DS babies are born to women under 35. So we’ll give Sarah a 20% chance of being Trig’s mom here (I know that this could be refined, either using conditional probability, which for various reasons I don’t want to apply, or better data regarding the probabilities, which I don’t have). But I think it’s important to remember that it’s simply a lot harder for women in their forties to produce babies at all (especially when they may have had their tubes seared shut, or when they’re grown-ups who should really understand birth control).
Data point/assumption 2: Sarah did not appear pregnant until her 7th month (unlike her daughter Bristol, who not only looked pregnant in the one picture which I saw of her, but mysteriously disappeared for the relevant period). I think this is rather unlikely – but there seem to be instances of it happening, even with women who have been pregnant before. So I’m assigning a 10% chance here, which I actually think is rather generous to Sarah, given how extremely odd the photos are. We’re down to 0.2 x 0.1 = 0.02 – a 2% chance that the child is hers.
Data point/assumption 3: Sarah did not tell anyone she was pregnant before then. Well, if she were faking it, she certainly wouldn’t tell anyone. However, I can imagine other reasons for not telling anyone. First, she had an important position, and she might not want to reduce her work effectiveness with a pregnancy. Second, knowing that it was a DS baby makes it less of an occasion of joy, especially if there is a chance that the baby won’t survive. So I’m not going to count this either for her or against her. We’re still at 2%.
Data point/assumption 4: Sarah did not behave pregnant before then, being seen drinking coffee and with no evidence of going to the doctor for extra visits. It’s possible that with a baby with Ds, that she saw no point in taking care of her body for him. On the other hand I think it’s odd that no one ever mentioned any behavior that would make them think, at least retroactively – Of course! Preggers! Especially as her appointments would have been generally visible to everyone on her staff, or at least there would have been occasions when people would wonder, hey, where was she Friday afternoon? Whereas poor Bristol apparently had a car accident in front of an OBGYN office. So again, being very generous to Sarah (and rather hard on everyone around her) I’m going to say 75%. We go from 0.02 x 0.75 = 0.015, or 1.5%
Data point/assumption 5: The flight attendants during Sarah’s wild ride claim that they did not notice that she was pregnant. Not just not 8 months pregnant, but pregnant at all! Now, if she was showing as much as she was in the Gusty photo, this seems really unlikely. Or if she took off an empathy belly, of course she wouldn’t appear pregnant either. However, I feel compelled to suggest another possibility: they noticed that she was pregnant but let her fly anyway, and then later, to protect themselves, said they didn’t notice anything. So on this point I’m not quite sure what to think – how to assess the odds. I’ll give it 50%, but additional input would be appreciated. That gets us down to .015 x 0.5 = 0.0075 or 0.75% (not 75%, but one hundredth of that)
Data point/assumption 6: the rest of the wild ride. Although I think it’s extremely peculiar, I’ll listen to the medical opinion you’ve presented here, and not go up or down. Still 0.75
Data point/assumption 7: Internet scrubbing. Many folks have mentioned that after the selection of Sarah as McCain’s VP candidate, pictures of Sarah disappeared, and that even kids’ computers and Myspace accounts were scrubbed. Although I could believe that the kids probably had indiscreet remarks on drugs and drinking, I can’t understand deleting general photos of Sarah. Something to hide? Sure looks like it, especially when you think that the McCain campaign would generally be interested in showing more rather than less of the photogenic Sarah officiating as governor … we’ll reduce her probability of telling the truth here by 50%. So that’s 0.0075 x 0.5 = 0.00375 or 0.375%
Data point/assumption 8: the letter from CBJ. This is a difficult item to assess. CBJ’s letter certainly indicates that Sarah gave birth to Trig. So for Sarah’s story to be false, CBJ would have to have lied. How likely is that? I have no idea. There are strange aspects to CBJ’s letter and behavior. Why on earth would she have OK’d the ride back from Texas? Heck, I can’t understand why she OK’d the ride TO Texas! Why was CBJ’s letter released on the eve of the election and not well before? Is it possible that there was a great deal of pressure on her? I’m sure that the letter was scrutinized by the McCain-Palin team – was she forced to say something which wasn’t true? Why did she need a lawyer when responding to questions from the ADN? This is all extremely odd, and it’s not as if we’ve never heard of unethical doctors, so I have some real doubts about CBJ. On the other hand, I must say that if Sarah was not pregnant, and all CBJ did was to lie about it, I actually respect her more. She did no medical harm in this situation and actually protected her patient’s privacy – probably ethically to her more important than telling the truth to the public. However, because I want to give her all benefits of doubts, I will double the chances that Sarah is telling the truth. So now it’s 0.00375 x 2 = 0.0075 or 0.75%
Data point/assumption 9: no release of a birth certificate. This I can’t understand at all. If Sarah is the mother, releasing the birth certificate would effectively quash all rumors. The only reason not to release it, other than Sarah not being the mother, would be if Todd were not the father – which I think is really unlikely. So here I have to give Sarah a 25% of telling the truth (generous to Sarah on my part): 0.0075 x 0.25 = 0.001875, or 0.1875%.
This is all very rough, but it ends up with Sarah having a less than 2 out 1000 chance of being Trig’s biological mother.
An interesting exercise for an afternoon – thanks for reading! UPDATE: Gryphen reminds me that he did a post on The Odds last year. It's a great read, as always, and free of numbers, which means I can wrap my tiny brain around it! Check it out!
And thank YOU, “V” for sharing your skills and time with us. Math wizards, weigh in!