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

### #1 Wannabelifeguard

Wannabelifeguard

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Posted 10 May 2020 - 11:44 AM

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?

### #2 OceanBreeze

OceanBreeze

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Posted 11 May 2020 - 04:58 AM

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.