If we assume that a police criminal profiler provides the following profile (and made up justifications) of a murder suspect:
Attribute 1: Killer is male
Justification: 90% of killers are male.
Attribute 2: Killer is unemployed
Justification: 90% of killers are unemployed
Attribute 3: Killer is an only child
Justification: 90% of killers are only childs
Attribute 2: Killer has no criminal convictions
Justification: 90% of killers have no criminal convictions
Remember, the stats are just made up.
How do I work out the probability the the entire profile is correct?
Should I treat all four attributes as dependent variables because 100% profile correctness depends on all attributes being correct? Something tells me that this is the wrong approach but I can't figure out why.
Or are the variables independent? I suspect this is the correct approach and the probability of the profile being 100% correct is 0.9 x 0.9 x 0.9 x 0.9 = 0.6561.