&gt; <i>If you are indeed close to the given description of a criminal complaint, they&#x27;re going to check. They have to check.</i><p>No, no they don&#x27;t. Goodness.<p>Let me break down this problem for you. Maybe a quarter of Boston is black, half of those are men, the height&#x2F;weight thing probably doesn&#x27;t rule out more than half the people (and the police clearly admit in this interaction that it&#x27;s a stretch to say he&#x27;s that light-weight). At least 10% of men will go out with a knit cap on a cold Boston day. You multiply those together and you get 0.00625. You, and the police officers, together are thinking, &quot;man, that&#x27;s a surprisingly low probability, only an 0.625% chance that we&#x27;d come across a guy matching that description! We&#x27;d better detain him!&quot;<p>But that&#x27;s a dangerous fallacy, in a family called the <i>false positive paradoxes</i>. Usually we surprise kids in statistics class with these by saying, &quot;hey, you live in New York and took a 99%-accurate test for HIV and it came out positive, what&#x27;s the chance that you actually have HIV?&quot; And they answer 99%. But the real answer is, you probably don&#x27;t have it, and the probability is closer to one in three. How can this be? Well, you can look up these statistics for 2012, where there are 130,000 cases of HIV&#x2F;AIDS in New York, which has nearly 20 million people, so your prior probability of having an HIV infection is only something like 0.65%; then the 1% false positive rate means that your 99%-accurate test has only increased your probability of actually having an HIV infection to about 39%, as the false positive set is larger than the true positive set.<p>It&#x27;s even worse in this case, where you&#x27;re looking for <i>one person</i>. Your 0.625% chance is spread out over a city of 650,000, meaning that over 4,000 people are subsumed by this description. Given all of the facts cited there is a less-than-0.025% chance that the guy they are detaining has done anything wrong.<p>Imagine the absurdity if they actually worked out and then quoted the statistics: &quot;Look, we&#x27;re 99.98% sure that you&#x27;re not the guy we&#x27;re looking for, but we&#x27;re detaining you anyway, because we demand <i>six nines</i> of certainty that you&#x27;re not who we&#x27;re looking for. Oh, you have a valid photo ID and we can easily check that someone with that name is a professor at this college? Roots in the community? Well, that only bumps you up to about 99.999% sure that you&#x27;re not the person we&#x27;re looking for, but that&#x27;s only <i>five nines</i>, buddy, not enough for us to let you go about your business. We&#x27;ve got to get the woman who made a complaint to look at your face to make absolutely sure that you&#x27;re not the criminal who we think you might with 0.001% chance be.&quot;<p>They absolutely do not <i>have to check</i> that. Certainly they don&#x27;t have to <i>stop you</i> to check that -- at five nines surely they can let you go about your business and check up with you at your residence if they receive sudden incriminating information.