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?
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
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:
extTotalstudyingeither=13+9+5=27
Finally, subtracting from the total number of students in the group:
extStudentsnotstudyingeither=29−27=2
Step 2
How many students in the tutor group study History?
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The total number of students studying History can be calculated by adding those studying only History and those studying both History and Geography:
extTotalstudyingHistory=13+5=18
Step 3
What is the probability that they study Geography but do not study History?
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
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(extGeographybutnotHistory)=299
Step 4
How many students study both Art and Physics?
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
From the diagram, it is clear that no students study both Art and Physics. Thus, the answer is 0.
