Theory of Probability HW #1 1. A hunter has two hunting dogs. One day, on the trail of some animal, the hunter comes to a place where the road diverges into two paths. He knows that each dog, independently of the other, will choose the correct path with probability p. The hunter decides to let each dog choose a path, and if they agree, take that one, and if they disagree, to randomly pick a path. Is his strategy better than just letting one of the two dogs decide on a path? 2. An electrical system consists of identical components that are operational with the probability p, independently of other components. The components are connected in three subsystems, as shown in the following figure. The system is operational if there is a path that starts at point A, ends at point B, and consists of operational components. This is the same as requiring that all three subsystems are operational. What are the probabilities that three subsystems, as well as the entire system, are operational? 3.
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