Are pairwise mutually exclusive events the same as mutually exclusive events? Larson (1982) defining the probability axioms talks about "mutually exclusive" events, while Poirier (1995) about "$A_1, A_2, \ldots$ as a sequence of pairwise mutually exclusive events events in the sigma-algebra $\tilde A$."
I suppose that the two notions are equivalent (they both refer two disjoint sets), right? Does this make adding the word "pairwise" superfluous on behalf of Poirier? 
Is there any other context out of probability that makes this distinction (using the word pair-wise) meaningful? According to wikipedia, in Logic, "pairwise mutually exclusive" means that both propositions cannot be true simultaneously, in contrast to just mutually exclusivity that means that if one is true, then the other cannot be true.
 A: What about vicious cycles? For example, suppose you have three binary random variables $A$, $B$, and $C$ that each take values $0$ or $1$. In this example, $A$ and $B$ are mutually exclusive if whenever $A = 0$, $B = 1$, and similarly for $C$.
$A$, $B$, and $C$ cannot all be pairwise mutually exclusive.
However, they can be "globally" mutually exclusive in the sense that, for example, if $A = 0$, then $B = 1$ and $C = 1$, and so on for the other variables.
I think that this counterexample proves that pairwise mutual exclusivity is not equivalent to mutual exclusivity.
A: Pick a three-letter word from an English dictionary. Let event A be, the word contains an "a"; let event E be, the word contains an "e"; let event I be, the word contains an "i".
A and E are not mutually exclusive ("are" contains both "a" and "e").
A and I are not mutually exclusive ("air" ....).
E and I are not mutually exclusive ("ire" ....).
So the three are not pairwise mutually exclusive, in fact, no pair is mutually exclusive. But the three are mutually exclusive, since no three-letter word contains all three letters.
A: 
Larson (1982) talks about "mutually exclusive" events, while Poirier
(1995) about "pairwise mutually exclusive events"
I suppose that the two notions are equivalent (they both refer two
disjoint sets), right? Does this make adding the word "pairwise"
superfluous on behalf of Poirier?

For simplicity, let's require the sample space to be finite and contain only possible outcomes, so that an empty event is precisely one that has zero probability (i.e., $P(S)=0\iff S=\emptyset$). With this, there appears to be two inequivalent definitions of mutual exclusivity (they converge only when discussing exactly two events):

*

*Gerry's and gideonite's answers on this page define multiple events as mutually exclusive iff no outcome belongs to all of them (e.g., for three events: $A\cap B\cap C=\emptyset$). In other words, a collection of mutually exclusive events is precisely a collection of events that cannot simultaneously occur.
[i.e., collectionwise mutual exclusivity]


*This answer, this answer, Wikipedia and mine define multiple events as mutually exclusive iff they are pairwise disjoint. In other words, a collection of mutually exclusive events is precisely a collection of events that can occur only one at a time.
[i.e., pairwise mutual exclusivity]
Definition 2 is stricter than Definition 1: observe that only the latter allows mutually exclusive events $A,B,C$ to be such that $A\cap B\ne\emptyset$ and such that $P(A)+P(B)+P(C)>1.$
Definition 2—but not Definition 1—is consistent with the definition of mutual independence, and the usual meaning of phrases like ‘mutual respect’, where mutual implies pairwise.
(However, note that while pairwise independence does not imply mutual independence, pairwise mutual exclusivity does imply both the above definitions of mutual exclusivity.)
P.S. Please refer to this answer for a parallel discussion of set disjointedness: Does ‘disjoint’ mean pairwise or collectionwise?. And in the answer ‘each’, ‘every’, ‘any’, ‘all’, I point out how the poor choice of the phrase ‘if any’ in Wikipedia's definition of the term ‘disjoint’ does not help disambiguate its definition!
A: They don't mean the same thing, but it is a short jump to show they are equivalent. A set of events, $A_1,...,A_n$ are mutually exclusive if the occurrence of one of them implies that the other $n-1$ events can't happen. It's immediate that the events are pairwise mutually exclusive. The other direction is immediate as well.
They aren't a priori the same, but it's immediate that they're equivalent.
A: Sets $A_1, A_2, ...$ are mutually disjoint if
$$\bigcap_{i=1}^{\infty} A_i = \emptyset $$
Sets $A_1, A_2, ...$ are pairwise disjoint if
$$A_i \cap A_j = \emptyset \ \forall i \ne j$$
Apparently, most texts use 'disjoint' to refer to 'pairwise disjoint'. Whenever a text uses 'pairwise disjoint', we can assume 'disjoint' refers to 'mutually disjoint'

In our case, 'mutually exclusive' by Larson means the same thing as 'pairwise mutually exclusive'. It depends on the text I guess.

See my questions:
Do Kolmogorov's axioms really need only disjointness rather than pairwise disjointness?
http://meta.math.stackexchange.com/questions/21560/should-these-be-simply-disjoint-instead-of-pairwise-disjoint
