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Shirley wants to find an estimate for the number of bees in her hive - Edexcel - GCSE Maths - Question 17 - 2020 - Paper 1
Question 17
Shirley wants to find an estimate for the number of bees in her hive. On Monday she catches 90 of the bees. She puts a mark on each bee and returns them to her hive.... show full transcript
Worked Solution & Example Answer:Shirley wants to find an estimate for the number of bees in her hive - Edexcel - GCSE Maths - Question 17 - 2020 - Paper 1
Step 1
Work out an estimate for the total number of bees in her hive.
Answer
To estimate the total number of bees in the hive, we can use the capture-recapture method.
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Let the total number of bees be denoted as .
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On Monday, Shirley captured and marked 90 bees.
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On Tuesday, she captured 120 bees, out of which 20 were already marked.
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We can set up a proportion:
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Cross-multiplying gives us:
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Solving for :
Thus, an estimate for the total number of bees in her hive is 540.
Step 2
If Shirley's assumption is wrong, explain what effect this would have on your answer to part (a).
Answer
If Shirley's assumption is wrong, meaning that some of the marked bees rubbed off between Monday and Tuesday, this would affect the accuracy of our estimate.
Specifically, if some marks were lost:
- Shirley would have over-estimated the number of bees in the hive.
- There would be fewer bees than estimated because the proportion of marked to unmarked bees would be skewed.
- Therefore, the estimated total of 540 bees would be higher than the actual number.