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72 students each took a theory test followed by a practical test - OCR - GCSE Maths - Question 8 - 2017 - Paper 1
Question 8
72 students each took a theory test followed by a practical test. They either passed or failed each test. This frequency tree shows some of the results. How many s... show full transcript
Worked Solution & Example Answer:72 students each took a theory test followed by a practical test - OCR - GCSE Maths - Question 8 - 2017 - Paper 1
Step 1
How many students passed both tests?
Answer
To determine how many students passed both tests, we first observe the number of students who passed the practical test, which is 52. The question implies that the number who passed both tests is the intersection of those who passed the theory test and the practical test.
Using a probability approach, we know that out of the total of 72 students, some must have passed both tests. We derive this from the frequency tree shown. Since 72 students took both tests, the number that passed the practical test (52) indicates that the remainder of the students must have failed at least one test. The exact number of students who passed both tests can then be calculated by establishing that the ratio of students passing the theory test influences the outcome.
Thus, the answer is 52, indicating that 52 students passed both tests.
Step 2
5/6 of the 72 students passed the theory test. Complete the frequency tree.
Answer
To find out how many students passed the theory test, we compute:
rac{5}{6} imes 72 = 60
This means that 60 students passed the theory test and consequently, the remaining:
students failed the theory test.
We can further analyze the practical test from the frequency tree, where from the 60 who passed the theory test, we already know that 52 passed the practical test. Hence, those who passed the theory test but failed the practical test equates to:
.
In total, the completed frequency tree would reflect:
- Passed Theory: 60
- Passed Practical: 52
- Failed Practical: 8
- Failed Theory: 12
- Passed Practical: 9
- Failed Practical: 3
Step 3
Which test was passed by more students? Explain your reasoning.
Answer
The practical test was passed by more students because out of the completed frequency tree:
- 52 students passed the practical test from the passing theory group.
- Also, 9 students from the failing theory group passed the practical test. Thus, the total number of students passing the practical test sums up to:
Comparatively, only 60 students passed the theory test, making the practical test the one that more students successfully passed.