Faiza is studying the population of rabbits in a park. She wants to estimate the number of rabbits in the park. On Monday she catches a random sample of 20 rabbits in the park, marks each rabbit with a tag and releases them back into the park. On Tuesday she catches a random sample of 42 rabbits in the park. 12 of the rabbits are marked with a tag. (a) Find an estimate for the number of rabbits in the park. Albie is studying the population of rabbits in a wood. One day, he catches 55 rabbits and finds that 40 of these rabbits are marked with a tag. Albie estimates there are 50 rabbits in the wood. (b) Explain why Albie's estimate cannot be correct.

GCSE Edexcel Maths Direct & Inverse Proportion: Faiza is studying the population

Faiza is studying the population of rabbits in a park - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 2

Question 15

Faiza is studying the population of rabbits in a park. She wants to estimate the number of rabbits in the park. On Monday she catches a random sample of 20 rabbits ... show full transcript

Worked Solution & Example Answer:Faiza is studying the population of rabbits in a park - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 2

Step 1

Find an estimate for the number of rabbits in the park.

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Answer

To estimate the total number of rabbits in the park, we can use the proportion of tagged rabbits in the second sample.

On Monday, Faiza tagged 20 rabbits.
On Tuesday, she catches 42 rabbits, of which 12 are tagged.
The proportion of tagged rabbits in the second sample is: $rac{12}{42}$
The estimate for the total population of rabbits (N) can be calculated by setting up a proportion: $\frac{12}{42} = \frac{20}{N}$
Cross-multiplying gives: $12N = 20 \times 42$
Solving for N: $N = \frac{20 \times 42}{12} = 70$

Thus, the estimate for the number of rabbits in the park is approximately 70.

Step 2

Explain why Albie's estimate cannot be correct.

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Answer

Albie catches 55 rabbits and finds 40 of them are tagged. From this, he calculates an estimate of 50 rabbits in total.

This estimate cannot be correct because:

The proportion of tagged rabbits in Albie's sample is: $\frac{40}{55}$
If all tagged rabbits were in Albie's sample, then this proportion should represent a larger population.
Extrapolating this proportion to estimate the total number would yield: $N = \frac{55 \text{ (sample size)}}{40 \text{ (tagged in sample)}} \cdot ext{(number of tagged)} = \frac{55}{40} \cdot 40 = 55$ which indicates the estimated population would be at least 55, leading to a contradiction since he uses 50.
Moreover, since he tagged 40 out of 55, it indicates that the total population must be larger than his estimate.

Therefore, Albie's estimate of 50 rabbits is not accurate.

Faiza is studying the population of rabbits in a park - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 2

Worked Solution & Example Answer:Faiza is studying the population of rabbits in a park - Edexcel - GCSE Maths - Question 15 - 2022 - Paper 2

Find an estimate for the number of rabbits in the park.

Explain why Albie's estimate cannot be correct.

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