Black bears (Ursus americanus) have a tendency to wander for food, and they have a high level of curiosity. These characteristics will sometimes get them into trouble when they travel through human-use areas such as parks. When they become "nuisances," the Park Service transplants them if possible to other areas. The outcomes of such transplants in Glacier National Park over a 10-year period are given in the table below:
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Transplanted Bear Table
|
|
|
Male
|
Female
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Totals
|
|
Successful
|
32
|
17
|
49
|
|
Returned to capture area
|
34
|
45
|
79
|
|
Nuisance in another area
|
14
|
4
|
18
|
|
Killed outside of park
|
3
|
4
|
7
|
|
Totals
|
83
|
70
|
153
|
a) From these data, estimate the probability that a randomly selected transplanted bear would be female or nuisance in another area.
b) After combining the above data with other National Parks, officials estimated that only about 18% of black bears in all parks become enough of a nuisance to be transplanted. They further estimate that 80% of nuisance bears are male, and 55% percent of non-nuisance bears are females. If a randomly selected bear is observed to be a male, what is the probability it will be a nuisance?