> if 900 out of 1000 people believe the OJ Simpson murdered Nicole Brown Simpson and 100 out of 1000 people believe he didn't, does this provide any useful info

> if 900 out of 1000 people believe the OJ Simpson murdered Nicole Brown Simpson and 100 out of 1000 people believe he didn't, does this provide any useful information about the likelihood that Simpson murdered Nicole Brown? Not in the same way. Note the key assumption in the accepted answer: a 10% false positive rate. That is, we assume (for good reason) that on average the population is fairly accurate at identifying and naming colors correctly. The analogous assumption in the OJ example would be "given media-filtered information about an emotionally-charged murder trial, most people accurately assess guilt with 90% probability." This is clearly false. But note that our entire criminal justice system does assume that "given all the facts as presented by a prosecutor and defense attorney over the course of a trial, people instructed to vote 'not guilty' unless they are sure of guilt 'beyond a reasonable doubt' will have a very low false positive rate." And here the exponent is only 12.