When dealing with collections of more than two events, in various applications, two notions of independence need to be distinguished. The events are called pairwise in- dependent if any two events in the collection are independent of each other. However, (overall) independence of events means, informally speaking, that each event is inde- pendent of any combination of other events in the collection. Consider two independent tosses of a fair coin. Let A be the event that the first toss results in heads, let B be the event that the second toss results in heads, and let C be the event that in both tosses the coin lands on the same side. Show that the events A, B, and C are pairwise independent that is, A and B are independent, A and C are independent, and B and Care independent. Also show that A, B, and C are not independent. Hint: Three events A, B, and Care independent if all of the four following constraints hold: P(AnB) = P(A)P(B), P(AnC) = P(A)P(C), P(BnC) = P(B)P(C), P(AnBnC) = P(A)P(B) P(C)