Independence and exclusive events

A fictional probability model tosses two independent fair coins and lists the four equally likely outcomes HH, HT, TH and TT. Event A is a head on the first coin, and event B is a head on the second. Another pair of events refers to exactly two heads and exactly zero heads in the same toss. One learner calls both pairs independent because the outcomes look different. Students must use the definitions, identify which events can occur together and compare the relevant probabilities rather than guess from wording. No biased coin, hidden dependence or sampling without replacement is part of the supplied model, and the exercise is not a claim about every real coin experiment.