Baggage screening equipment has a 99% probability of detection of a prohibited item in a bag that contains such an item, and a false detection probability, that is, the probability of detecting a prohibited item in a bag that does not contain such an item, is 0.05. Assume the probability of a bag containing a prohibited item is 0.005. What is the probability of finding a prohibited item in a bag in a particular screening cycle? What is the probability of a false detection in a particular screening cycle? Assume that the equipment screens 5000 bags per day. On the average,

(a) How many prohibited items are there?

(b) how many are detected and found? and

(c) how many detected and not found, that is, false detection?