We can show with a few assumptions that the police thought that the prior probability of the leaves being marijuana (before the field test) is at least 41%. A

We can show with a few assumptions that the police thought that the prior probability of the leaves being marijuana (before the field test) is at least 41%. A = leaves in trash are marijuana B = field test result is positive First use Bayes' to get P(A|B) = P(B|A)P(A) / [P(A)P(B|A)+P(-A)P(B|-A)] Assume the false positive rate, P(B|-A) = 0.7. Assume the true positive rate, P(B|A) = 1. The result is P(A) = 0.7P(A|B)/(1-0.3P(A|B)) Assume to get a warrant the police need P(A|B)>0.5. This puts P(A)=0.41. However, probable cause is more strict. Assume we need P(A|B)>0.90. This puts P(A)=0.86. So if you go to a garden store and you drink tea, the police are 86% sure there are illegal substances in your home.