KnowledgeBoat Logo
|

Mathematics

An ornithologist wants to estimate the number of parrots in a large field. She uses a net to catch some, and catches 32 parrots, which she rings and sets free. The following week she manages to net 40 parrots, of which 8 are ringed.

(i) What fraction of her second catch is ringed?

(ii) Find an estimate of the total number of parrots in the field.

Mathematical Modelling

2 Likes

Answer

(i) Given,

Ornithologist manages to net 40 parrots, of which 8 are ringed.

Fraction of ringed = 840=15\dfrac{8}{40} = \dfrac{1}{5}.

Hence, 15\dfrac{1}{5} of her second catch is ringed.

(ii) We may apply the idea of marking and recapture to determine the overall number of parrots in the field. According to the theory, the percentage of marked parrots in the second catch corresponds to the percentage of marked parrots in the overall population.

Let's use N to represent the overall number of parrots in the field. The first batch, as said, caught 32 parrots and ringed every single one of them. In the second batch, there were 8 ringed parrots out of 40 caught. We can set up a proportion :

⇒32N=840⇒N=32×408⇒N=32×5⇒N=160.\Rightarrow \dfrac{32}{N} = \dfrac{8}{40} \\[1em] \Rightarrow N = \dfrac{32 \times 40}{8} \\[1em] \Rightarrow N = 32 \times 5 \\[1em] \Rightarrow N = 160.

Hence, total number of parrots in the field are 160.

Answered By

3 Likes

Related Questions