Probability of an event basedon given variables.

[FrankJ777]

For some time now I've been trying to figure out probably for a problem of the following form.

Say a criminal profiler is trying to determine the probability that someone is a criminal based on statistical information.

60% of people who have mustaches are criminals.
70% of people who wear black hats are criminals.
80% of people who wear sunglasses are criminals.

If the profiler is profiling an individual who wears sunglasses, a black hat, and has a mustache; how would she determine the probability that this individual is a criminal?

By the way, this is not a homework problem, I'm just trying to understand how to apply probability better.
Thanks a lot.

 

[ImaLooser]

For some time now I've been trying to figure out probably for a problem of the following form.

Say a criminal profiler is trying to determine the probability that someone is a criminal based on statistical information.

60% of people who have mustaches are criminals.
70% of people who wear black hats are criminals.
80% of people who wear sunglasses are criminals.

If the profiler is profiling an individual who wears sunglasses, a black hat, and has a mustache; how would she determine the probability that this individual is a criminal?

By the way, this is not a homework problem, I'm just trying to understand how to apply probability better.
Thanks a lot.

The events may or may not be independent. If they aren't independent, then there is no answer other than collecting data and measuring it directly.

 

[FrankJ777]

Could one at least establish an upper or lower probability limit? Would the individual in the example have at least a 80% probability of being a criminal based on the criteria that 80% of people who wear sunglasses are criminals? On the other would the probability of the individual being a criminal be at least 60% based on the "fact" that 60% of people with mustaches are criminals?

 

[mathman]

80% would be lower limit.
If the criteria are independent, then the probability of being a criminal is
1 - prob(at least one does not hold) = 1 - .4x.3x.2 = 97.6%.