Final answer:
In the context of probability and tossing a fair coin twice, the question seeks to determine p(a ∩ b'), where event (a) is exactly one tail, and event (b) is at least one tail. The probability of such an intersection, where we look for an outcome that is exactly one tail and not at least one tail, is zero, as event (b) already includes the outcomes of event (a).
Step-by-step explanation:
The subject of this question is Mathematics, specifically probability. The question pertains to the probabilities associated with tossing a fair coin twice. When a fair coin is tossed twice, there are four possible outcomes HH (both heads), HT (first head, second tail), TH (first tail, second head), and TT (both tails). Event (a) is defined as observing exactly one tail which includes the outcomes HT and TH. Event (b) is described as having at least one tail, which includes HT, TH, and TT. The intersection of event (a) and the complement of event (b) (p(a ∩ b')) is actually an impossible event (null set) because event (b) includes all the outcomes that event (a) includes and more.
Therefore, an event that is exactly one tail and not ('complement of' or ') at least one tail' does not exist. Both events share the same outcomes where there is one tail, as the definition of 'at least one tail' encompasses the possibility of exactly one tail. P(a ∩ b') is thus zero because there are no outcomes that satisfy this intersection.