P1: OTA/XYZ P2: ABC
JWST061-02 JWST061-Caers March 30, 2011 18:55 Printer Name: Yet to Come
2.4 PROBABILITY 17
Interpretation 2: The geologist assesses, based and his/her expertise and prior knowl-
edge, that it is more likely that the region will contain iron ore. In fact, 60/100 is a quan-
titative measure of the geologist’s assessment about the hypothesis that the region will
contain iron ore, where 0/100 means there is certainly no iron ore and 100/100 means
there is certainly iron ore.
Interpretation 1 is also termed the frequency interpretation. Probability is interpreted
as the ratio of success in the outcome of a repeated experiment, although in practice, such
repetition need not be made explicit.
Probability = (# of successful events)/(total number of trials)
For interpretation 2, probability is not thought of as being the property of an outcome
(i.e., whether or not iron ore is actually found). Rather, it is considered to be a non-
mathematical assessment based on prior knowledge by the person making the statement.
In this book, both interpretations are used. For example, we will present modeling
techniques to figure out what the probability of contamination of a drinking well is given
the available data. To do so, a number of alternative Earth models will be created, some
of which show contamination some of them not; the frequency of contamination is inter-
preted as a probability. In the same context, however, geologist will need to decide what
geological depositional system is present in order to create such Earth models. Consider
that there is some discussion between a fluvial and an alluvial system being present. Since
only one actual system is present, any probabilistic statement such as “the probability of
the system being fluvial is x %” is not based on any frequency but on a personal assess-
ment from the expert geologist based on his/her prior knowledge when interpreting the
available data.
2.4.2 Sample Space, Event, Outcomes
Consider again the diamond example data set above. Taking a single stone from the de-
posit is considered the experiment; one also terms this “sampling” a stone. The outcome
of the experiment is not known with certainty ahead of time. However, assume that the
weight of a diamond is less than a big number, “BIG,” but larger than zero. The set of all
possible outcomes is also termed the sample space (S). For example:
Sizes of Diamonds: S = (0, BIG)
Race: S ={asian, black, caucasian,...}
Any subset of this sample is termed an event:
Event E
1
={a diamond of size larger than 5 ct}
Event E
2
={a diamond of size between 2 and 4 ct}