Estimation problem

Question

A group of scientists in an observatory catch, tag, and then release 50 butterflies. The next day, they catch 100 butterflies and observe that 10 of them are tagged. Which of the following is the best estimate for the total of butterflies at the observatory?

A) 140

B) 150

C) 200

D) 500

 

Note : i know the answer is D but i dont know why ?!

I want to know the concept of the solution.

Answer 1

Think of this as taking a sample of the butterfly population and we are estimating that the proportion of the population that are tagged is 10/100 or 10%.  But we know we tagged 50 of them.  So we would expect that the true population proportion tagged would be close to 10% as well.

 So  50/ Population = .10  or Population = 50/.10  =  500  Hope this helps.  Terry