5.4.2 The prosecutor Fallacy Revisited

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5.4.2 The prosecutor Fallacy Revisited

Apache
Hi,

Could someone clarify something for me with regards to section 5.4.2 of the book?

If About 1 in 1000 people have this blood type.
Then how do we come to the value of P(E|H) = 1/1000?
Shouldn't we use the 10,000 male population to calculate P(E|H) as such:

No of people having the blood type = 1/1000 * 10,000 = 10
then 9 out of 10 persons have the same blood type but are innocent = 9/10
=> P(E|H) = 0.9

Am i missing something very fundamental over here?



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Re: 5.4.2 The prosecutor Fallacy Revisited

Apache
Correction:

9 people are innocent hence P(E|H) = 1/9 instead of 9/10?
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Re: 5.4.2 The prosecutor Fallacy Revisited

norman@eecs.qmul.ac.uk
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In reply to this post by Apache
The value P(E | H) is the probability that a person not connected with the crime would have the same matching blood type as that found at the scene. This is 1/1000 because we are assuming that blood type occurs in 1 in a 1000 people. In 10,000 people we expect about 10 to have the matching blood type. In the absence of any other evidence any one of the 10 people is no more likely than the other 9 to have committed the crime. This is where the approximate 9/10 probability of innocence comes in once you have the evidence. i.e. this is where P(H | E) is about 0.9 (the fact it is actually 0.91 is due to some more explicit assumptions needed as shown in the calculatons on page 124).

Norman Fenton
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Re: 5.4.2 The prosecutor Fallacy Revisited

Apache
If 10 out of 10,000 have the same blood group, can we say that the 10 comprises of:
1) 9 innocents
2) 1 culprit

Hence if we have 9 innocents, and we want to get the probability of seeing the evidence if the person is innocent, so instead of taking P(E|H) = 10/10,000 = 1/1000 = (0.001)
can we take P(E|H) = 9/10,000 (0.0009)? to be more accurate.



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