Final answer:
Events A, B, C, and D are not mutually exclusive because B and C share a common outcome 'f'. Thus, these events can occur simultaneously, which precludes them from being mutually exclusive.
Step-by-step explanation:
To determine whether the events A, B, C, and D are mutually exclusive, we need to check if any pair of these events share common outcomes. Mutually exclusive events cannot occur at the same time — they do not share outcomes, which means the intersection of the events must be empty, and the probability of their intersection is 0.
Here, we are given the sample space S = {a, b, c, d, e, f, g, h, i, j} and events A = {a, b, c}, B = {d, e, f}, C = {f, g}, and D = {h, i, j}. We notice that events A and C do not share any outcomes, and neither do A and D, or B and D. However, events B and C both contain the element 'f', and therefore, they are not mutually exclusive. Since at least one pair of these events is not mutually exclusive, the entire collection of events A, B, C, and D cannot be considered mutually exclusive.
The correct answer is: (Choice B) A, B, C, and D are not mutually exclusive.