Shuster (1991) describes a number of probability calculations that he did for a court case…

Shuster (1991) describes a number of probability calculations that he did for a court case involving the sale of cocaine. A Florida police department sized 496 suspected packets of cocaine, of which four were randomly selected and tested and found to actually be cocaine.. the police then chose tow more packets at random and posing as drug dealers, sold the packets to the defendant. These last two packets were lost before they could be tested to verify that they were, indeed, cocaine.

(a) If the original 496 packets were composed of N packets of cocaine and M = 496 –N noncocaine, show that the probability of selecting 4 cocaine packets and then 2 noncocaine packets, which is the probability that the defendant is innocent of buying cocaine, is

(b) Maximizing (in M and N) the probability in part (a) maximizes the defendant’s “innocence probability”. Show that this probability is .0022, attained at M = 165 and N =331

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