## July 15, 2009

**PLEASE, MONTY HALL, LET ME SWITCH FROM GOAT TO BABY**

Last week, I got obsessed with probability problems. Since my likelihood of having a successful pregnancy is 50/50, it mirrors coin toss statistics. I originally wrote that I had a 6.25% chance of a fourth miscarriage, but I kept thinking about the problem and realized that was too simplistic. That assumed that I had four chances to get pregnant and struck out on all four. But that wasn't the case: in fact, I had 22 chances to get pregnant, got pregnant on four of them, and flipped tails on the first three.

One of my good friends is a statistician, so I contacted her and asked her a coin toss problem: Let's say you flip a coin 22 times and mark down whether each flip is heads or tails. What is the probability that I could choose four random flips -- say numbers 8, 13, 19, 22 (the months I got pregnant) -- and have them all be tails?

She thought about it and replied:

(11 choose 4) / (22 choose 4) = 330 / 7315 = 4.511%

Explanation: The number of ways to select 4 tails out of 11 possible tails divided by the number of ways to select 4 coins out of 22 possible coins.

(11 choose 4) = 11! / (4! * 7!) = 330

(22 choose 4) = 22! / (4! * 18!) = 7315

My gut feeling was right that the probability was even lower than it would've been with just four coin tosses (though I know enough about stats to know my gut isn't always right; otherwise, we'd all get goats.)

Anyway, I've been obsessing about this for a while. I would start to feel confident that surely I wouldn't get so unlucky again, but then I would reign myself back in. When it happens to someone theoretical, it's a statistic; when it happens to you, it's a tragedy.

In the car on the way there today, I was certain I would get bad news. I was a wreck. I had to share another ultrasound room, which nearly sent me into a rage until I realized the other girl was only there to check her follicles. Luckily this time, it seemed that the hospital staff actually knew who I was and knew to tread lightly. They were all nice and at least acted like they had read my chart five seconds before coming in the room. They were sorry my husband was gone and expressed hope that this time would work out better than the others.

And it appears that, for now, Schroedinger's cat is alive.

Luckily, their sympathy extended to extra medical attention too: I get to have weekly ultrasounds. I go back next Wednesday morning to see if the baby is still alive then too. If it's still alive in two weeks, that will be the furthest I've ever progressed. I won't begin to feel relaxed at all until then, but for now, I'll take whatever good news I can get.

And I can go back to feeling bad and sad.

Posted by: Sarah at
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You know I'm around no matter what. And, God love ya, you knew better than to ask this girl about math. Watched me struggle one too many times to figure out a decent tip, eh?

Lurve you!

Posted by: Guard Wife at July 15, 2009 11:29 AM (M+hWl)

Posted by: Wifeunit at July 15, 2009 12:11 PM (+2Ggg)

Posted by: David Boxenhorn at July 15, 2009 12:26 PM (AZIQI)

Posted by: dutchgirl at July 15, 2009 12:45 PM (hLAkQ)

There are two things at work here: the probability of GETTING pregnant and the probability of STAYING pregnant.

Yes, my odds of getting pregnant in any individual month remain the same as any other human female: 1 in 4. I have roughly borne that out with my 4 pregnancies in 22 ovulations.

Once I am pregnant, the odds of staying that way are the 50/50.

I'm considering "eggs" as flips, not "pregnancies." Each egg is a coin toss. Each pregnancy is more complicated than that. And the flips that you don't look at DO matter if the question you're asking is "what are the odds I still haven't had a healthy baby after 22 ovulations?" instead of "what are the odds I'll keep this baby I am carrying right now?"

I know each successive egg has no bearing on the next, just like coins don't, but cumulatively, I should've theoretically put out 11 good eggs over these past 2 years, but none of those managed to fertilize. So it's more than just four flips, cumulatively. It's 22 flips.

As my stats friend said, picture this:

Let's say you have these two different sequences of 22 coin tosses (keeping with your example of T on the 8th, 13th, 19th, and 22nd tosses):

1) H T H T H T H T H T H T T H H T H T T H H T

2) H H H H H H H H T H H H T H H H H H T H H T

The probability of randomly selecting 4 tails out of these two sequences is different.

Even though both scenarios could be what has happened to me over the past 2 years, I should theoretically be closer to the first. (Setting aside the fact that we have no way of knowing if my eggs are evenly distributed at all, that is to say that 25% are normal, 25% are balanced, 25% are unbalanced 7, and 25% are unbalanced 22. It should work out in theory over 100,000 eggs, but who's to say that it really does?)

I am no math expert, but I respectfully think you're wrong. I think it's more complicated than just four chances...

Posted by: Sarah at July 15, 2009 01:03 PM (TWet1)

I saw the problem the way David did, assuming that past outcomes had no effect on future ones. However, at the moment, I think it's more complicated than that. What's the chance of you being pregnant in any given month? I'm no statistician, but I doubt it's just 50% - or that it's even calculable. The probability of your current situation involves that figure, whatever it is, as well as the 50/50 per pregnancy.

Thank you for reprinting the details of how your friend got the answer instead of simply giving us the answer. I may use (x choose y) methodology for my own coin toss problems in the future.

I am impressed by your mental versatility which is evident even from the last few posts. Politics, poetry, statistics ... what don't you do?

Posted by: Amritas at July 15, 2009 01:07 PM (+nV09)

Prayers continue, and all of that.

I keep thinking and praying for each of you....

I know you want to move forward, and I know you want future, and i know you want to start walking forward..

Posted by: awtm at July 15, 2009 02:28 PM (mYtP/)

I don't understand what your question actually is, though. Now it seems to me like it's "what is the chance of getting tails four times in a row when I try to flip 22 times, and the chance of successfully flipping is 1/4"? But that question really doesn't make sense to me because it seems like the interesting question would be "what is the chance of getting all tails when I try to flip 22 times, and the chance of successfully flipping is 1/4".

Posted by: David Boxenhorn at July 15, 2009 02:31 PM (AZIQI)

Second, you are right...there are two variables at work in this situation. Getting pregnant and staying pregnant. And, while your previous pregnancies have no true bearing (in a statistical sense) on your current pregnancy (or any subsequent pregnancies), they do establish a (really crappy) pattern.

For simplicity's sake, I'd round to the middle and say 5%. Which is better than 0% (for the 'glass is half full' population here) but truly sucks monkey balls (for those with a more practical outlook on life...some might call us cynical) when all you really want is a baby.

Sorry to ramble - I've been working in my Calculus study guide and my brain is stuck on numbers. I'm praying hard and looking forward to hopeful news next Wednesday. (I may be in a cynical mood these days but I'm still an optimist at heart).

Posted by: HomefrontSix at July 15, 2009 02:32 PM (7Qxzl)

I am assuming that I have had somewhere around 11 good eggs over the past 22 months, and just lamenting the fact that out of those 11 good ones, I never managed to get pregnant during those months. I always got pregnant during bad egg months. The probability of *that* seems to be 4.5%, and it gnawed at me for a week.

Anyway, you're right in the sense that none of this matters anymore and I'd just like to concentrate on the 50% chance I currently have!

Posted by: Sarah at July 15, 2009 02:42 PM (TWet1)

Posted by: Ruth H at July 15, 2009 02:51 PM (4u82p)

The expected number of coin flips is 5.5 (22/4). The chance of getting all tails is 1/(2 ^ 5.5) = 2.2%. But I think it's wrong since I don't think the chance of getting pregnant is really 1/4.

In any case, you're right: You're past all that now.

Posted by: David Boxenhorn at July 15, 2009 02:52 PM (AZIQI)

Posted by: Mare at July 15, 2009 02:54 PM (HUa8I)

Posted by: Sarah at July 15, 2009 03:15 PM (TWet1)

Wait a minute, your prego now, 100%. Yea, yea, I know about the last times, forget that for now (with all due respect), your 100% prego NOW. Screw all that and that mind numbing math, the glass is half full...NOW.

Remember, only Liberals and losers (excuse the redundancy) are pessimistic.

Posted by: tim at July 15, 2009 03:28 PM (nno0f)

1) I love the way your mind works... with the statistics.

2) I'm praying my butt off for you and S's cat.

Posted by: Val at July 15, 2009 05:42 PM (5btL/)

Posted by: rc at July 16, 2009 12:07 AM (aJX4Q)

I've been thinking of you almost constantly the last few days. I suspect if all the hope, love and good thoughts I'm sending your way could truly affect fertility, you'd be having octuplets about now...

*holding my breath for you*

Posted by: FbL at July 16, 2009 12:42 AM (HwqvF)

Posted by: deskmerc at July 16, 2009 03:00 AM (pYOXQ)

I am too dumb to get the statistics. But I can relate, definitely, to waiting for the other shoe to drop, as so many have after multiple miscarriages.... You're on my mind!

Posted by: Allicadem at July 20, 2009 07:21 PM (nlT4X)

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