A designer conducts random searches to detect criminals, and may condition the

search probability on individuals' appearance. She updates her belief about the

distribution of criminals across appearances using her search results, but incorrectly

takes her sample distribution for the population distribution. In equilibrium she

employs optimal search probabilities given her belief, and her belief is consistent

with her findings. We show that she will be discriminating an appearance if and only

if she overestimates the probability of this appearance's being criminal. Moreover,

in a linear model, tightening her budget will worsen the situation of those most

discriminated against.