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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