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Jeat is growing carrots from seed in his garden - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Question 4
Jeat is growing carrots from seed in his garden. He plants 28 carrot seeds but only 12 grow. Jeat says The probability of one of my carrot seeds growing is $ rac{3... show full transcript
Worked Solution & Example Answer:Jeat is growing carrots from seed in his garden - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Step 1
Use Jeat's result to show that he is correct.
Answer
To verify Jeat's statement, we calculate the probability of a carrot seed growing based on the data provided:
The total number of seeds planted by Jeat is 28, and the number of seeds that grew is 12. The probability of one seed growing can be calculated as:
ext{Probability} = rac{ ext{Number of Seeds that Grew}}{ ext{Total Seeds Planted}} = rac{12}{28}
Simplifying this fraction:
rac{12 ext{ (divided by 4)}}{28 ext{ (divided by 4)}} = rac{3}{7}
This confirms that Jeat's claim of the probability being rac{3}{7} is indeed correct.
Step 2
How many seeds should he plant?
Answer
Using Jeat's probability of growth, rac{3}{7}, we can determine how many seeds the farmer needs to plant to expect 10,000 successful carrots.
First, we set up the equation to find the number of seeds he should plant (let's call it ):
rac{3}{7} imes x = 10000
To isolate , we rearrange the equation:
x = 10000 imes rac{7}{3}
Calculating this gives:
\approx 23333.33$$ Since the number of seeds must be a whole number, the farmer should plant approximately 23334 seeds.Step 3
Explain why it may not be sensible for the farmer to use Jeat's experimental probability to calculate the number of seeds he should plant.
Answer
Using Jeat's experimental probability may not be sensible due to several factors. Firstly, the growing conditions on the farm may differ significantly from those in Jeat's garden, which could lead to a different success rate for seed germination. Additionally, Jeat's sample size is relatively small (only 28 seeds), which may not provide an accurate representation of the probability. A larger sample size would give more reliable data about growth rates.