# Probability of an event basedon given variables.

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.

Related Set Theory, Logic, Probability, Statistics News on Phys.org
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.

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