Calculating Probabilities
Calculating the probability that a given alternative will be successful
requires logic and experience. The more accurately we can determine
probability, the more intelligently we select among alternatives.
However, this type of calculation necessarily involves a certain
amount of subjectivity.
Begin with the weather. If your alternative is based on the wind
remaining below 3 mph and in its current quarter, for example, then
determine, through experience or consultation, the likelihood that
the wind will change. Let’s say that figure is 10% -- once
in every ten similar circumstances, the wind will change. Fire behavior
is another area in which chance plays a role. Based on your own
observations, imagine that you calculate that the chance of spotting
is near 0 under current conditions, but that spotting will occur
one time in 5, were the wind to shift and increase. The deployment
of your resources ensures that if spotting occurs, your strategy
will fail. What is the probability of failure in this instance?
To put it another way, what is the probability that the wind will
change and that spotting will occur? To calculate the probability
of both events occurring, we multiply, so our calculation becomes:
10% x 20% = 2% (.10 x .20 = .02)
Pretty good odds, in fact. If we have multiple events which must
all occur in order to bring about failure, we continue to multiply:
Pa x Pb x Pc … Pn
Where Pa is the probability that event A will occur, Pb is the probability
that event B will occur, and so on through N, which is the last
event in our chain.
If we have two independent factors which lead to failure, we need
to handle them somewhat differently. If we have a strategy that
will fail if the weather changes (10%), or if we are unable to get
necessary resources (5%), we need to add the probability of those
events, and then subtract the product to determine the likelihood
that one or the other of those events will occur:
(10%+5%)-(10% x 5%)aa (15%) aa- aa(.5%)a= 14.5% (.10+.05)-(.10 x
.05)aa(.15)aa- aa(.005)a= .145
Calculating the probabilities of combinations of events more complex
than this gets rather involved, and is beyond the scope of this
training program. Be aware that calculating probabilities is not
as simple as it may seem! If you are interested in learning more,
you may wish to consult a textbook on probability and statistics,
or look within your agency for assistance.
If we think about these examples, they seem logical. The probability
that two events will occur is significantly less than the probability
that one event or the other will occur. The more contingent events
need to occur simultaneously, the smaller the probability that that
will happen. On the other hand, we can’t just add probabilities
to see if one event or another might occur. If the probability of
one event was 75%, and the probability of another was 50%, we would
suspect that something was wrong if we calculated a 125% probability
that one of these events would happen. 100% is all we get!
These examples are fabrications, but you get the idea. Try to predict
the different ways in which your alternative strategy may fail,
estimate the probability of each, and calculate as appropriate.
There is still an element of subjectivity in your calculations,
but at least you will be able to explain them to others
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