I was recently given the following statistics: On a particular highway, 18% of drivers are black, 63% of drivers searched by the police are black. So, a black driver is 7.7 times more likely to be searched.
I'm having some difficulty deriving the figure 7.7 myself. Am I correct to interpret the 63% as the conditional probability of being black given that you have been searched by the police as being 0.63? Thus, 0.37 as the probability of not being black given that you have been searched by the police.
Furthermore I'm not sure how we would arrive at the probability of being searched given that you are black (in order to make the comparison and arrive at 7.7). Or is this even the correct probabilistic interpretation of the sentence?
(if anyone is interested, this data is from an economics paper by Knowles, Persico and Todd, 2001)