Do criminals do those things much more frequently than non-criminals?
In Spain 86% of phone buyers buy from the top 5 brands. Pixel is not among those. Only 1.7% buy Pixel phones. Police say that they have observed that among criminals the percent with Pixels is much higher.
Suppose police have a dead store clerk and only 3 people who could have possibly done it, and those people are 1 Pixel owner, 1 Samsung Galaxy owner, and 1 Apple iPhone owner. Given that criminals are buying Pixels at a rate higher than the general population does, and assuming they are not buying Galaxies and iPhones at a higher rate, can the police use that in statistically valid way to help their investigation?
The answer is yes.
Let (c) = the probability that a random phone owner in Spain is a criminal.
Let (p) = the probability that a random phone owner owns a pixel, which is 0.017 in Spain.
Let (p|c) = the probability that someone owns a Pixel given that they are a phone owning criminal. Police say that this is higher than 0.017, but they do not give a number. I'd expect they wouldn't really notice if it was only a little higher. I'd guess it would need to be at least 0.05 for them to notice, so let's go with that. If someone finds a better number it is easy to adjust in the following calculations.
Let (c|p) = the probability that someone is a criminal given they have a Pixel.
Bayes' Theorem tells us that (p|c)(c) = (c|p)(p).
Rearrange that to get (c|p) = (p|c) (c) / (p). Plugging in 0.05 for (p|c) and 0.017 for (p) gives:
(c|p) = 2.9 (c)
In our case with 3 people to investigate, one with a Pixel and two without, if we are sure that one of them must be the criminal the probability that it will be the Pixel owner is 59.2%. It is 20.4% for the Galaxy owner and 20.4% for the iPhone owner [1]. If the police don't have the resources to investigate all 3 in parallel they should check out the Pixel owner first.
[1] Actually, I don't think that is quite right. I think that because I added the condition that we are sure it must be one of them the distribution will change slightly. It still should be close though.
Please read about Bayes' theorem. If 50% of criminals use the os, and 1% of population it is goodnpoint to check any the OS owner. The same way Police Will check your id if you Wear robbery mask, or sell small packets on the Street.
