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9 children are asked whether they have a laptop or an iPad - OCR - GCSE Maths - Question 9 - 2018 - Paper 4
Question 9
9 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.
Worked Solution & Example Answer:9 children are asked whether they have a laptop or an iPad - OCR - GCSE Maths - Question 9 - 2018 - Paper 4
Step 1
Represent this information on a Venn diagram.
Answer
To represent the given information on a Venn diagram, we need to identify the number of children in each category:
- Total Children: 72
- Children with Laptops: 31
- Children with iPads: 48
- Children with Both: 12
- Children with Neither: 5
From this, we can extract the following figures:
- Only Laptops: Children with Laptops - Children with Both = 31 - 12 = 19
- Only iPads: Children with iPads - Children with Both = 48 - 12 = 36
We can now place these figures into the Venn diagram accordingly:
- Label the left circle as "Laptops".
- Label the right circle as "iPads".
- Inside the Laptop circle but outside the overlapping area, write 19.
- Inside the iPad circle but outside the overlapping area, write 36.
- In the overlapping area, write 12.
- Outside both circles, write 5.
Step 2
Write down the probability that they have an iPad but not a laptop.
Answer
To find the probability that a randomly chosen child has an iPad but not a laptop, we use the following information:
- Only iPads: 36 (those who have iPads but do not have laptops).
- Total Children: 72.
The probability is calculated as: ext{Probability} = rac{ ext{Number of children with iPads but not laptops}}{ ext{Total number of children}} = rac{36}{72} = rac{1}{2}
Thus, the probability that a child chosen at random has an iPad but not a laptop is rac{1}{2}.