Should you take into account the possibility that the chicken was just something transfigured before increasing the probability of Dumbledore being a Sadist?
No, for a qualitative change in various probabilities we can ask if Dumbledore has unpleasant associations with burning—like a memory of something he wishes he didn’t (have to) do, or of a sad time for his family. These would reduce the chance that he sees “setting fire to a chicken” as clever.
Seems like a sadistic DD who killed Narcissa would enjoy alluding to this event, in a way that would disturb Harry without making him suspect the purpose behind it. But that seems to me like a more complicated hypothesis than a Dumbledore who shares Donny’s suspicions, given that DD looks like a ‘bad guy’ of a radically different kind.
Ok, I’m a bit lost here, I haven’t dealt with probabilties for several years and would like to find out where I was wrong. Please correct my reasoning:
P(Dumbledore did it \bigcap Dumbledore is a Sadist) =P (Dumbledore did it) x P(Dumbledore is a Sadist)
P(Dumbledore did it)=1-P(Dumbledore didn’t do it)
P(Dumbledore didn’t do it)=P(Dumbledore didn’t do it | He burned a real chicken) + P(Dumbledore didn’t do it | He burned something transfigured to be a chicken).
Now, we don’t know the probabilities P(He burned a real chicken) and P(He burned something transfigured to be a chicken), but it is something that has to be taken into account, isn’t it?
@your answer
In your answer, you assume he did it. If he didn’t do it, he wouldn’t neccessarily have negative associations with burning, only with the fact of being thought to have burned her.
If I understand you correctly, your reasoning regarding unpleasant associations with burning already assumes that he did it.
If he didn’t do it (and we don’t know yet wether it was him or, for example, Amelia Bones), he wouldn’t have unpleasant associations with the method of Narcissa’s death, only with the fact that it was ascribed to him. So there is the possibility that he didn’t do it, and doesn’t have negative associations with burning that would be brought up when burning transfigured stones or tablecloth or whatever.
Should you take into account the possibility that the chicken was just something transfigured before increasing the probability of Dumbledore being a Sadist?
No, for a qualitative change in various probabilities we can ask if Dumbledore has unpleasant associations with burning—like a memory of something he wishes he didn’t (have to) do, or of a sad time for his family. These would reduce the chance that he sees “setting fire to a chicken” as clever.
Seems like a sadistic DD who killed Narcissa would enjoy alluding to this event, in a way that would disturb Harry without making him suspect the purpose behind it. But that seems to me like a more complicated hypothesis than a Dumbledore who shares Donny’s suspicions, given that DD looks like a ‘bad guy’ of a radically different kind.
Ok, I’m a bit lost here, I haven’t dealt with probabilties for several years and would like to find out where I was wrong. Please correct my reasoning:
P(Dumbledore did it \bigcap Dumbledore is a Sadist) =P (Dumbledore did it) x P(Dumbledore is a Sadist)
P(Dumbledore did it)=1-P(Dumbledore didn’t do it)
P(Dumbledore didn’t do it)=P(Dumbledore didn’t do it | He burned a real chicken) + P(Dumbledore didn’t do it | He burned something transfigured to be a chicken).
Now, we don’t know the probabilities P(He burned a real chicken) and P(He burned something transfigured to be a chicken), but it is something that has to be taken into account, isn’t it?
@your answer In your answer, you assume he did it. If he didn’t do it, he wouldn’t neccessarily have negative associations with burning, only with the fact of being thought to have burned her.
If I understand you correctly, your reasoning regarding unpleasant associations with burning already assumes that he did it.
If he didn’t do it (and we don’t know yet wether it was him or, for example, Amelia Bones), he wouldn’t have unpleasant associations with the method of Narcissa’s death, only with the fact that it was ascribed to him. So there is the possibility that he didn’t do it, and doesn’t have negative associations with burning that would be brought up when burning transfigured stones or tablecloth or whatever.