An article in The American Statistician (May 1991) described the use of probability in a reverse cocaine sting. Police in a midsize Florida city seized 496 foil packets in a cocaine bust. To convict the drug traffickers, police had to prove that the packets contained genuine cocaine. Consequently, the police lab randomly selected and chemically tested 4 of the packets; all 4 tested positive for cocaine. This result led to a conviction of the traffickers. 

a. Of the 496 foil packets confiscated, suppose 331 contain genuine cocaine and 165 contain an inert (legal) powder. Find the probability that 4 randomly selected packets will test positive for cocaine. 

b. Police used the 492 remaining foil packets (i.e., those not tested) in a reverse sting operation. Two of the 492 packets were randomly selected and sold by undercover officers to a buyer. Between the sale and the arrest, however, the buyer disposed of the evidence. Given that 4 of the original 496 packets tested positive for cocaine, what is the probability that the 2 packets sold in the reverse sting did not contain cocaine? Assume the information provided in part a is correct.

c. The American Statistician article demonstrates that the conditional probability, part b, is maximized when the original 496 packets consist of 331 packets containing genuine cocaine and 165 containing inert powder. Recalculate the probability, part b, assuming that 400 of the original 496 packets contain cocaine.