The chief of a fire department is trying to decide what to do to protect the community against a forest fire. The fire is huge and she does not have enough firefighters to send everywhere. Forest fires can be strengthened by the wind. Weather reports predict a 30% chance that the wind will be from the north, a 50% chance that the wind will be from the northwest, and a 20% chance that the wind will be from the west. If the wind is from any other direction, or if there is rain, the whole community is certain to be safe. The probability of rain is 10%. She could tell her firefighters to build a protective firebreak near the biggest town in the community or to build a firebreak near a small village. Here is what will happen if there is no rain. If she builds the firebreak near the town then homes will be destroyed in the village; if the wind is from the north 25 homes will be destroyed in the village, while if the wind is from the west or northwest 150 homes will be destroyed in the village. Alternatively, if she builds the firebreak near the village then 100 homes will be destroyed in the town if the wind is from the west or northwest, or 200 homes will be destroyed in the town if the wind is from the north.

1.In the fire chief case, what is the probability that the whole community will be safe?

2.What should the fire chief do? and why she should do that.?

3.Now suppose that the fire chief decided to build the firebreak at the town because she was very concerned that the largest settlement in the community might be harmed and wanted to be sure that the town would be safe. To people who complain that she is abandoning the people of the village who will quite possibly lose their homes, the chief says that she is doing what needs to be done to ensure that there will be no catastrophe.

Assess the fire chief's reasoning.