Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

Comments on Why "only 1/10,000 men with wives they abuse subsequently murder them" ≠ P(A|G,M) & "50% of husbands who murder their wives abused them” ≠ P(G|A)?

Post

Why "only 1/10,000 men with wives they abuse subsequently murder them" ≠ P(A|G,M) & "50% of husbands who murder their wives abused them” ≠ P(G|A)?

+0
−4

All emboldings are mine. See my red side line — the solution identifies "only 1 in 10,000 men with wives they abuse subsequently murder their wives" (in the problem statement) with $\color{red}P(G|A)$.

See my green underline — the solution identifies "50% of husbands who murder their wives previously abused them" with $\color{limegreen}P(A|G,M)$.

But why not vice versa? Why doesn't "only 1 in 10,000 men with wives they abuse subsequently murder their wives" correspond to $\color{limegreen}P(A|G,M)$, and "50% of husbands who murder their wives previously abused them" $\color{red}P(G|A)$?

☣ 2.8.2 (Defense attorney's fallacy). A woman has been murdered, and her husband is put on trial for this crime. Evidence comes to light that the defendant had a history of abusing his wife. The defense attorney argues that the evidence of abuse should be excluded on grounds of irrelevance, since only 1 in 10,000 men with wives they abuse subsequently murder their wives. Should the judge grant the defense attorney's motion to bar this evidence from trial?

Suppose that the defense attorney's 1-in-10,000 figure is correct, and further assume the following for a relevant population of husbands and wives: 1 in 10 husbands abuse their wives, 1 in 5 murdered wives were murdered by their husbands, and 50% of husbands who murder their wives previously abused them. Also, assume that if the husband of a murdered wife is not guilty of the murder, then the probability that he abused his wife reverts to the unconditional probability of abuse.

How to define the "relevant population" and how to estimate such probabilities are difficult issues. For example, should we look at citywide, statewide, national, or international statistics? How should we account for unreported abuse and unsolved murders? What if murder rates are changing over time? For this problem, assume that a reasonable choice of the relevant population has been agreed on, and that the stated probabilities are known to be correct.

Image alt text

Blitzstein. Introduction to Probability (2019 2 ed). pp 75-76.

History
Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

2 comment threads

Would it be possible to change the context of the problem so the mathematical principles stay the sam... (2 comments)
By definition? (3 comments)
Would it be possible to change the context of the problem so the mathematical principles stay the sam...
HDE 226868‭ wrote over 2 years ago

Would it be possible to change the context of the problem so the mathematical principles stay the same but we don't have a question mentioning abuse and murder? I know it was the author's decision, but I feel like you could still rephrase the issue you're having.

DNB‭ wrote over 2 years ago

I'd rather not "rephrase the issue you're having", because I want to stick to the text in the book. Have you thought of complaining to the author at blitzstein@stat.harvard.edu?