Solving Tree Diagram Problem - Exam Missed

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ok so what am i doing wrong here? this was the only question i missed on my exam, and its driving me crazy...

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For (b) I'd have put (95+8-N)/100000 where N is the (unspecified) number of pet owners that are bitten by pets that are not their own and also bitten by their own pet.
 
I would have thought he would be after P(Bitten by own pet|Bitten) which would be 87/95
 
Sounds reasonable. But now I think the answer is 95/103.
 

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