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In Vitro Fertilization Probabilities w/ Binomial Expansion: HELP HELP!!! - Math Lovers United

About In Vitro Fertilization Probabilities w/ Binomial Expansion: HELP HELP!!!

Previous Entry In Vitro Fertilization Probabilities w/ Binomial Expansion: HELP HELP!!! Jan. 20th, 2009 @ 10:30 pm Next Entry
Female family member has to get in vitro fertilization. Doctors say she's got a 10% chance of each fertilized egg becoming viable and that the odds of each is independent from the odds of the rest being successful. To reckon the odds that at least one will take, I took the odds of all failing (each being 1.0-0.1=0.9) for 1-0.9^4=0.3439 or 34%. There's a wrinkle.

She's a hard-core, but not insane, pro-lifer: any viable fertilized egg is a life that cannot be murdered. Thus, doing six eggs runs the risk of too many kids; too few wrecks the odds of a successful kid; and the procedure is freakin' expensive.

IIRC, I can figure out the odds of each possible set of successes & failures using the binomial expansion, but I'm not sure I remember how to do it. If she's doing four eggs, is this the proper way to figure out the odds of 0 successes, 1 success,...,4 successes?

(.1+.9)^4 = .1^4 * .9^0 + 4(.1^3 * .9^1) + 6(.1^2 * .9^2) + 4(.1^1 * .9^3) + .9^4

where each term is the odds of that number of successes & failures. So for (success, failure):

(4, 0) = .0001 or .01%
(3, 1) = .0036 or .36%
(2, 2) = .0468 or 4.68%
(1, 3) = .2916 or 29.16%
(0, 1) = .6561 or 65.61%

Which, if I'm adding correctly, doesn't quite add up to 100%, but is close enough, I guess.

Have I done this correctly? If so, I simply use the expansion for the fifth- and sixth-powers for five or six eggs, correct?

Please let me know ASAP! I just found out about this tonight, and she really wanted to know how all the probabilities worked out, and I think it's important to know. I only have a couple of days to give all this to her, so please let me know. She may be a hard-core pro-lifer, but I want to help her be the smartest one she can be! ^_^

Thank you so much!!!

^_^
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From:mathteacher
Date:January 21st, 2009 05:18 am (UTC)
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under your stated given conditions, i believe that your analysis is correct.

in general, if p is the probability of success per trial, the probability of exactly r successes in n trials is C(n,r) * p^r * (1-p)^(n-r), where C(n,r)=n!/(r!(n-r)!).

i am, however, skeptical that the probabilities for each fertilized egg becoming viable are in fact independent when implanted simultaneously, but it's probably a negligible difference.
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From:js_africanus
Date:January 21st, 2009 06:12 am (UTC)

Independent Eggs

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Thank you so much!

I agree that independence seems sketchy, but that's what the doc apparently told my sister, so that's what I've got to go on.

I once saw an online lecture about teaching probability through surprising results, and the lecturer said that it's almost impossible to teach probability to engineers, since they've taken a little calculus and think they know everything. In my experience doctors aren't much better.

(Read "Calculated Risks" by Gerd Gigerenzer and try phrasing to the doctor the odds as Gigerenzer explains, and you'll realize that for med school, statistics is merely an intelligence test and not something to actually be learned. No joke. I've tried it; it's disheartening.)

Anyway, thanks much!
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From:digitig
Date:January 21st, 2009 10:29 am (UTC)

Re: Independent Eggs

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I once saw an online lecture about teaching probability through surprising results, and the lecturer said that it's almost impossible to teach probability to engineers, since they've taken a little calculus and think they know everything.
I think the lecturer meant "because their brains are already full" :-)

I find it a strange claim, actually, because engineers have to work a lot with probability nowadays, and they'd struggle to qualify as engineers if they didn't understand probability at least reasonably well. Perhaps the lecturer was making the common mistake in the English speaking world of confusing technicians with engineers. Or maybe they were thinking of old-school engineers who were much more about making and much less about analysis.

Why, yes, I am an engineer as it happens...
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From:js_africanus
Date:January 21st, 2009 02:42 pm (UTC)

Re: Independent Eggs

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...they'd struggle to qualify as engineers if they didn't understand probability at least reasonably well.

Taking stats courses doesn't mean they understand the subject. See ITE Code 814 for reference: the "bible" of traffic engineering is risking people's lives on the basis of a comically bad regression.
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From:digitig
Date:January 21st, 2009 03:13 pm (UTC)

Re: Independent Eggs

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I've no idea what ITE Code 814 is or where I might see it, but I have seen some appalling probability blunders written into regulations by bureaucrats (and I've been in a standardisation meeting where the chair insisted that the question of whether a pure Poisson process is time stationary be put to a vote, rather than just checking any elementary textbook) -- and I've seen the engineers lumbered with implimenting those regulations wince, because they realise that they'll have to do every job twice: once the right way so that things work, and again the wrong way to satisfy the regulators. Duff standards doesn't tell you whether engineers understand probability, it tells you which engineers can most readily be spared from their normal work to sit on the committees.
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From:js_africanus
Date:January 21st, 2009 03:53 pm (UTC)

Re: Independent Eggs

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...and I've been in a standardisation meeting where the chair insisted that the question of whether a pure Poisson process is time stationary be put to a vote....

That's insane.

[pissy, grumpy mode]

I'd be more sympathetic if I weren't dealing with a shopping-center application where the traffic engineer is trying to help the developer kill people by basing designs on a traffic volume regression of four data points, three of which are dominated by an outlier.

Honestly, it beggars belief — talk some sense into traffic engineers for me, will 'ya? Here's how it works for them. Choose a land use. Then sit and count peak-hour traffic for that land use. Do that a few times and run a regression of traffic against size on those results. Now the coefficient on size becomes a strictly deterministic Fact, with a capital eff, and is treated as such.

[/pissy, grumpy mode]

Anywho, be well!
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From:digitig
Date:January 21st, 2009 04:45 pm (UTC)

Re: Independent Eggs

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Honestly, it beggars belief — talk some sense into traffic engineers for me, will 'ya? Here's how it works for them. Choose a land use. Then sit and count peak-hour traffic for that land use. Do that a few times and run a regression of traffic against size on those results. Now the coefficient on size becomes a strictly deterministic Fact, with a capital eff, and is treated as such.
Well, of course, it is a strictly deterministic fact, the question is, what fact? For one thing, it's an expected value of the coefficient on size, which will have confidence bounds (I've often thrown people who insist I demonstrate that the probability of an undesired event is less than some specified value into a spin by asking them "to what confidence do I need to demonstrate it?") And it's the expected value at the times the observation was made -- is it subject to diurnal or seasonal variation? And so on. But it is a strictly deterministic fact, just not the one that they want. Anyway, we seem to have strayed from probability into statistics :-)
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From:js_africanus
Date:January 21st, 2009 05:10 pm (UTC)

Re: Independent Eggs

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Have you heard about the engineer who lived around the time of the French Revolution? People who felt they were being guillotined unjustly would lie down facing upward, and if the guillotine didn't work, it was considered providence of God and they were spared. So when an unjustly condemned engineer followed a few people who were spared, he looked up at the mechanism, saw what was wrong with it, and explained how to fix it...
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From:digitig
Date:January 21st, 2009 06:09 pm (UTC)

Re: Independent Eggs

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That "engineer" would be Malabonce in the 1966 Carry On film "Don't Lose Your Head", wouldn't it?
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From:js_africanus
Date:January 21st, 2009 07:02 pm (UTC)

Re: Independent Eggs

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I couldn't say. My uncle, an engineer, told me the story when I was a little kid, and I think it was supposed to illustrate the ethos of the engineer.
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Date:June 10th, 2010 09:36 am (UTC)

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