Two cold tablets are unintentionally placed in a box containing two aspirin tablets. The four tablets are identical in appearance. One tablet is selected at random from the box and is swallowed by the first patient. A tablet is then selected at random from the three remaining tablets and is swallowed by the second patient.

Give the collection of simple events that define the events below:

The sample space S

The event A that the first patient obtained a cold tablet

The event B that exactly one of the two patients obtained a cold tablet

The event C that neither patient obtained a cold tablet

By summing the probabilities of simple events, find P(A), P(B), P(AB), P(AB), P(C), P(AC), and P(AC).