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40% chance of cloudy, and a 45% chance of sunshine. Note that these weather
outcomes are mutually exclusive and collectively exhaustive .Theyaremutu-
ally exclusive in that there is no overlap in events; that is, it is either rainy or
cloudy or sunny. They are collectively exhaustive in that the sum of their prob-
abilities of occurrence is equal to 1; that is, these are all the outcomes that can
3. Since weather determines attendance, Voitech interviews Fr. Eﬁa with the intent
to determine his estimates for attendance given the various weather conditions.
Based on his previous experience with parish events, Fr. Eﬁa believes that if
weather is rainy , attendance will be 1500 people; if it is cloudy , attendance
is 2500; if the weather is sunshine , attendance is 4000. Of course these are
subjective estimates, but he feels conﬁdent that they closely represent likely
4. The selection of the games remains the same—Omnipotent Two-Sided Die
(O2SD), Wheel of Outrageous Destiny (WOD), and the Bowl of Treachery (BT).
To simplify the process and to correspond with Fr. Eﬁa’s wishes to limit gam-
bling (recall he does not approve of gambling), he will insist that every attendee
must play all three games and play them only once. Later he may consider relax-
ing this condition to permit individuals to do as they please—play all, some,
none of the games, and to possibly repeat games. This relaxation of play will
cause Voitech to model a much more complex event by adding another factor of
uncertainty: the unknown number and type of games each attendee will play.
5. He also has set the odds of attendees winning at the games as follows: proba-
bilities of winning in O2SD, WOD, and BT, are 20, 35, and 55%, respectively.
The structure of the games is quite simple. If an attendee, wins Fr. Eﬁa gives
the attendee the value of the bet (more on this in 6.); if the attendee, loses then
the attendee gives Fr. Eﬁa the value of the bet. The logic behind having a single
game (BT with 55%) that favors the attendees is to avoid having attendees feel
as if they are being exploited. He may want to later adjust these odds a bit to
determine the sensitivity of gambling revenues to the changes.
6. All bets at all games are $50 bets, but he would also like to consider the possi-
ble outcomes of other quantities, for example $100 bets. This may sound like a
substantial amount of money, but he believes that the very afﬂuent attendees will
not be sensitive to these levels of bets.
7.4.3 Resolution of Weather and Related Attendance
Now that the Vegas Night at OLPS is precisely speciﬁed, we can begin to model the
behavior of the event. To do so, let us ﬁrst use another form of inﬂuence diagram,
one that considers the uncertain events associated with a process. This diagramming
approach is unlike our initial efforts in Exhibit 7.5 and it is quite useful for identify-
ing the complexities of uncertain outcomes. One of the advantages of this approach
is its simplicity. Only two symbols are necessary to diagram a process: a rectangle