Finite Math Question

(B) is NOT a possible sample space for this experiment.


A sample space Ω contains all the possible outcomes of an experiment.


According to the description, we analyze as follows:
(A)
One of these 6 possible situations occurs, this set of these 6 outcomes form a sample space of the experiement.

(C)
Either the pair (F1, S1) is chosen, or not, so this set of 2 outcomes form a sample space of the experiement.

(D)
Since the subcommittee must have one member from each group, and for the faculty group, there is only F1 or F2, so either F1 is chosen or F2 is chosen. That is, the set of 2 outcomes form a sample space of the experiement.


Going back to (B), this set contains 5 elements where each element refers to a particular member. However, the experiment is to draw two members with each from each group. The 5 elements do not show the possible outcome of the experiment so (B) is not a sample space for this experiment.

Note that you should also contrast this claim with (D).
For (D), the two elements form a partition of the sample space where exactly either one occurs in the experiment, so I also regard that as a sample space.
For (B), the 5 elements (if you regard F1 as F1 being chosen) are exhastive events in the sample space, but they are not mutually exclusive. For example, if the outcome is (F1, S1), then both the elements F1 and S1 refer to the events that occur.
Therefore, I think (B) is not a proper sample space for this experiment.