This Venn diagram shows the number of students in a Year 10 tutor group who study History (H) and Geography (G). There are 29 students in the tutor group. (i) How many students in the tutor group do not study History or Geography? (ii) How many students in the tutor group study History? (iii) One of the 29 students is selected at random. What is the probability that they study Geography but do not study History? (b) This diagram represents students in a tutor group who study Art (A) and Physics (P). How many students study both Art and Physics?

GCSE OCR Maths Probability: This Venn diagram shows the numb

This Venn diagram shows the number of students in a Year 10 tutor group who study History (H) and Geography (G) - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

Question 10

This Venn diagram shows the number of students in a Year 10 tutor group who study History (H) and Geography (G). There are 29 students in the tutor group. (i) How ... show full transcript

Worked Solution & Example Answer:This Venn diagram shows the number of students in a Year 10 tutor group who study History (H) and Geography (G) - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

Step 1

How many students in the tutor group do not study History or Geography?

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Answer

To determine how many students do not study History or Geography, we first identify the total number of students studying either subject using the Venn diagram. The values are as follows:

Students studying only History: 13
Students studying only Geography: 9
Students studying both History and Geography: 5

Calculating students studying either subject:

$ext{Total studying either} = 13 + 9 + 5 = 27$

Finally, subtracting from the total number of students in the group:

$ext{Students not studying either} = 29 - 27 = 2$

Step 2

How many students in the tutor group study History?

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Answer

The total number of students studying History can be calculated by adding those studying only History and those studying both History and Geography:

$ext{Total studying History} = 13 + 5 = 18$

Step 3

What is the probability that they study Geography but do not study History?

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Answer

To find this probability, we focus on students who study Geography but not History. This includes only those studying Geography exclusively:

Students studying only Geography: 9

The probability is given by the ratio of students studying Geography but not History to the total number of students:

$P( ext{Geography but not History}) = \frac{9}{29}$

Step 4

How many students study both Art and Physics?

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Answer

From the diagram, it is clear that no students study both Art and Physics. Thus, the answer is 0.

This Venn diagram shows the number of students in a Year 10 tutor group who study History (H) and Geography (G) - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

Worked Solution & Example Answer:This Venn diagram shows the number of students in a Year 10 tutor group who study History (H) and Geography (G) - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

How many students in the tutor group do not study History or Geography?

How many students in the tutor group study History?

What is the probability that they study Geography but do not study History?

How many students study both Art and Physics?

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