I'm not sure how to start this problem. Can anyone describe what the steps to solving a problem like this are? Not looking for answers to the problem, but rather a method to solve these problems.
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a) What is the probability of a forest fire?
b) What is the probability that there is a storm given that there is a forest fire?
c) What is the probability of a camp fire and a forest fire?
Thanks
This is a tree diagram, and the probabilities given are the probabilities of moving along a given branch; however, some of the branches are not explicitly shown, which is possibly confusing. Here is an illustration of how to use the diagram and interpret the probabilities.
What is the probability that you will observe thunder? Looking at the probabilities, you may hear thunder whether or not you see lightning, you may see lightning whether or not there is a storm, and there may or may not be a storm. So one way to hear thunder is to have a storm and see lightning, and then hear thunder. There is a .1 probability of a storm, then given that you have a storm there is a .5 probability that you see lightning, and given that you see lightning there is a .95 probability that you hear thunder. So this particular path through the tree has a probability of .1*.5*.95=.0475; the probabilities multiply. We are using a theorem which says that P(A and B) = P(A)*P(B|A)
But this is not the only way to hear thunder. There might be no storm, you might see no lightning, but you still hear thunder. The probability here is .9*.95*.2 = .171. Note that it is more likely to hear thunder for no apparent reason than to hear it in the kind of obvious situation. This should not surprise you, it is a common experience to hear distant thunder and all there is to see is some dark clouds far away. And there are still more ways to hear thunder. So far our total probability of thunder is .0475+.171=.2185, but this is not complete.
Try to finish this up and then think about the question you were asked, i.e. probability of a forest fire. Part (b) needs Bayes' theorem, we can talk about that later.
