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72 children are asked whether they have a laptop or an iPad - OCR - GCSE Maths - Question 27 - 2018 - Paper 1
Question 27
72 children are asked whether they have a laptop or an iPad. • 31 have a laptop. • 48 have an iPad. • 12 have both. • 5 have neither. (a) Represent this informatio... show full transcript
Worked Solution & Example Answer:72 children are asked whether they have a laptop or an iPad - OCR - GCSE Maths - Question 27 - 2018 - Paper 1
Step 1
Represent this information on a Venn diagram.
Answer
To create the Venn diagram, we need to determine the number of children who own only a laptop, only an iPad, and both.
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Both (laptop and iPad): 12 (given)
- This is the intersection of the two circles in the Venn diagram.
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Only a laptop:
- Total with laptops = 31
- Those with both = 12
- Therefore, only laptops = 31 - 12 = 19.
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Only an iPad:
- Total with iPads = 48
- Those with both = 12
- Therefore, only iPads = 48 - 12 = 36.
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Neither: 5 (given)
Summarizing the information in the Venn diagram:
- Number of children with only laptops = 19
- Number of children with only iPads = 36
- Number of children with both = 12
- Number of children with neither = 5.
Step 2
Write down the probability that they have an iPad but not a laptop.
Answer
The number of children who have an iPad but not a laptop is 36 (as calculated above).
Total number of children surveyed = 72.
Thus, the probability that a randomly chosen child has an iPad but not a laptop is given by:
So, the final answer is: ( \frac{1}{2} )