| Relative Likelihood |
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| • | Now
suppose we don't know the probability of a stiff neck, |
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| but
we do know: |
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| – | the
probability of whiplash P(W) = (1/1000) |
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| – | the
probability of a stiff neck given whiplash P(S|W) = 0.8 |
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| • | What
is the relative likelihood of meningitis and whiplash |
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| given
a stiff neck? |
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| • | Write
Bayes' Rule for each and write P(M|S)/P(W|S) |
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| • | P(M|S)/P(W|S)
= (P(S|M)P(M)/P(S)) / (P(S|W)P(W)/P(S)) |
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| = (P(S|M)
P(M))/(P(S|W) P(W)) |
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| =
(0.5*(1/50000))/(0.8*(1/1000)) |
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| = .00001 /
.0008 = 1/80 |
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