Photo AI
Students at a school must choose one subject from Option 1 and one from Option 2 - OCR - GCSE Maths - Question 16 - 2017 - Paper 1
Question 16
Students at a school must choose one subject from Option 1 and one from Option 2. The school offers two languages, French and Spanish. The subjects are given in thi... show full transcript
Worked Solution & Example Answer:Students at a school must choose one subject from Option 1 and one from Option 2 - OCR - GCSE Maths - Question 16 - 2017 - Paper 1
Step 1
Total subject combinations
Answer
To determine the total number of subject combinations, we can list the subjects from both options:
- Option 1: French, Art, Music, Economics
- Option 2: Spanish, Geography, History
Calculating combinations:
- Option 1 subjects: 4
- Option 2 subjects: 3
Thus, the total combinations = 4 (from Option 1) × 3 (from Option 2) = 12 combinations.
Step 2
Combinations with exactly one language
Answer
A subject combination has exactly one language if it includes either French or Spanish and excludes the other. The valid combinations are:
- French and Geography
- French and History
- Art and Spanish
- Music and Spanish
- Economics and Spanish
Counting these combinations yields 5 valid combinations with exactly one language.
Step 3
Calculate percentage
Answer
To find the percentage of subject combinations with exactly one language:
a) Use the formula for percentage:
total valid combinations = 5
total combinations = 12
o Per cent = ( \frac{number\ of\ valid\ combinations}{total\ combinations} \times 100 )
o Percentage = ( \frac{5}{12} \times 100 \approx 41.67% )
Therefore, the percentage of all subject combinations which have exactly one language is approximately 41.67%.