From: Lee Corbin (lcorbin@tsoft.com)
Date: Wed Jul 09 2003 - 00:48:32 MDT
Dan writes
> > p(deformity) = 0.01
> > p(~deformity) = 0.99
> > p(rubella|~deformity) = 0.1
> > p(rubella|deformity) = 0.5
> > p(rubella&~deformity) = p(r|~d)p(~d) = .1*.99 = .099
> > p(rubella&deformity) = p(r|d)p(d) = .5*.01 = .005
> > p(rubella) = p(r&d) + p(r&~d) = .104
> > p(deformity|rubella) = p(rubella&deformity)/p(rubella) = .005/.104 = .048
>
> Now, wait a minute.
> You begin with p(deformity) = 0.01. I presume that's your interpretation
> of the claim that "a newborn will have deformities traceable to a sickness
> of its mother during pregnancy", but that doesn't seem right to me at all.
> [Obviously p(deformity) should include cases where there are deformities
> that aren't traceable to a sickness of the mother.]
That's right.
> Here's my interpretation of the problem.
>
> p(deformity&traceable) = 0.01
> p(rubella|~deformity) = 0.1
> p(rubella|deformity&traceable) = 0.5
>
> Where the question is: what's p(deformity|rubella)?
>
> Now, perhaps I can assume that deformity&rubella entails traceable,
> but I can't just assume that deformity->traceable.
Whyever should you even assume that deformity&rubella implies traceable?
The infant may have a deformity that is not traceable to a sickness
of the mother, and yet the mother might still have rubella anyway.
Besides, this is supposed to be a *math* problem, not a medical exam.
(Though in other arguments with some here, I have hypothesized that
if it's a *statistics* problem, then it can be claimed that it is
your responsibility to know or find out all the relevant research;
it's necessary, they say, to have correct priors.)
> (And let's not even get into the possibility that the child
> may not be "born healthy and normal" but may have no "deformities".)
If "deformities" does not mean the exact opposite of "born
healthy and normal", then we should give up on word problems,
and just formulate all problems with symbols alone. You have
to assume that the writers of the problem are attempting to
communicate clearly.
Lee
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