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Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later

Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?
 
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1 Answer

Based on studies of populations, we can expect the number of bears in the sample to represent the general population in proportion. Write a proportion to express this relationship letting the number of bears in the total population be b.
 
Use the ratio of tagged bears to total number of bears in the proportion.
 
Ratio
 tagged  
  total
 
Write the proportion:
Sample          Population
    2        =        50   
   100                 b
 
Solve the proportion for b:
 
2b = 5000
b = 2500
 
We can expect that there are 2,500 bears in the Keweenaw Peninsula.