The madman murders only almost always. It is possible but vanishingly unlikely that he just never rolls snake eyes (or he runs outside of the total population with the growth so he can’t get a full patch). Option 1 doesn’t care whether the doom ultimately happens while option 2 assumes that the doom will happen.
The proper enlish version of option two would be “Given that the dice came up snake eyes and that you were kidnapped at some point what is the probabilty that it did so while you were kidnapped?”. Notice also that this is independent off what dice readings result in doom. That is if the world is only saved on snake eyes the chance is still “only” 9⁄10.
The madman murders only almost always. It is possible but vanishingly unlikely that he just never rolls snake eyes (or he runs outside of the total population with the growth so he can’t get a full patch). Option 1 doesn’t care whether the doom ultimately happens while option 2 assumes that the doom will happen.
The proper enlish version of option two would be “Given that the dice came up snake eyes and that you were kidnapped at some point what is the probabilty that it did so while you were kidnapped?”. Notice also that this is independent off what dice readings result in doom. That is if the world is only saved on snake eyes the chance is still “only” 9⁄10.
Note that
P(you are in batch t | murders batch t & you are kidnapped)
cannot be 9⁄10 for all t; in fact, this probability must go to 0 in the limit as t → infinity, regardless of what prior you use.