Probability - Chances That This Criminal Profile Is 100% Correct?

[Wannabelifeguard]

Hi guys,

 

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.

 

Any thoughts?

[OceanBreeze]

Hi guys,

 

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.

 

Any thoughts?

 

 

You multiply the individual probabilities, as you did 0.9 x 0.9 x 0.9 x 0.9 = 0.6561 You do this whether they are dependent or independent variables.

 

But this does not guarantee the profile is 100% correct. There is never such a guarantee when dealing with probability.