In a large company, there are 500 electronic systems installed. Each of them is either connected to a network (N) or functions as a separate unit (U). Also, some of them have incorporated a new high-speed device (H) while the remaining ones operate on an older, low-speed device (L). The frequencies for each of the four combinations above in the set of 500 systems are as follows:

N U H 280 70 L 130 20 An engineer selects a system at random for inspection.
(i) If she finds out that the system is connected to the network, what is the probability that it operates on the high-speed device?
(ii) If she finds out that the system operates as a unit, what is the probability that the system operates on the low-speed device?
(iii) If she discovers that the system operates on the high-speed device, what is the probability that it is connected to the network?
(iv) If she discovers that the system operates on the low-speed device, what is the probability that it is connected to the network?
Using your results from the above parts, verify that the following is not true for two events A and B on a sample space:
P(A|B′) = 1 − P(A|B).
Give an intuitive explanation for this fact.