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120 students in Year 10 and Year 11 sit a test - OCR - GCSE Maths - Question 6 - 2019 - Paper 4
Question 6
120 students in Year 10 and Year 11 sit a test. - 61 of the students are in Year 10. - 83 of the students are right-handed. - 20 of the students in Year 11 are left... show full transcript
Worked Solution & Example Answer:120 students in Year 10 and Year 11 sit a test - OCR - GCSE Maths - Question 6 - 2019 - Paper 4
Step 1
Calculate left-handed students in Year 10
Answer
To determine the number of left-handed students in Year 10, we first find the total number of students in Year 10:
Total in Year 10 = 61
Out of the total 120 students, 83 are right-handed, which means:
Total left-handed students = Total students - Right-handed students = 120 - 83 = 37.
Assuming the left-handed students are equally distributed among Year 10 and Year 11, we can denote:
Let L10 be left-handed students in Year 10 and L11 be in Year 11.
Thus, if Year 11 has 20 left-handed students, to find the left-handed students in Year 10, we can conclude that:
L10 + L11 = 37, where L11 = 20 implies L10 = 17.
Step 2
Step 3
Calculate probabilities
Answer
Now we compute the probabilities of selecting a left-handed student from each year:
For Year 10:
Probability (Year 10) = ( \frac{L10}{\text{Total in Year 10}} = \frac{17}{61} \approx 0.278 ) or (27.8%).
For Year 11:
Probability (Year 11) = ( \frac{L11}{\text{Total in Year 11}} = \frac{20}{59} \approx 0.339 ) or (33.9%).
We can conclude that Year 11 has a higher probability of selecting a left-handed student because ( 33.9% > 27.8% ).
Step 4