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The table shows the children nominated to win the subject prize in Mathematics and the subject prize in English - OCR - GCSE Maths - Question 6 - 2019 - Paper 1
Question 6
The table shows the children nominated to win the subject prize in Mathematics and the subject prize in English. | Mathematics | English | |-------------|---------... show full transcript
Worked Solution & Example Answer:The table shows the children nominated to win the subject prize in Mathematics and the subject prize in English - OCR - GCSE Maths - Question 6 - 2019 - Paper 1
Step 1
Identify the total combinations
Answer
To find the total combinations of winners for both prizes, we have the following:
- There are 4 candidates for the Mathematics prize (Alice, Ben, Emma, Paddy).
- There are also 4 candidates for the English prize (Alice, Claire, Gabi, Simon).
Therefore, the total combinations of winners are:
Step 2
Calculate combinations with Alice winning
Answer
Now we identify the combinations where Alice wins at least one prize.
-
Alice wins Mathematics:
- English winners can be Alice, Claire, Gabi, or Simon: 4 combinations.
-
Alice wins English:
- Mathematics winners can be Ben, Emma, or Paddy: 3 combinations (since Alice winning Mathematics is already counted).
Thus, the total combinations where Alice wins at least one prize are:
Step 3
Calculate the percentage
Answer
Finally, to find the percentage of combinations in which Alice wins at least one prize, we use the formula:
ext{Percentage} = rac{ ext{Number of favorable outcomes}}{ ext{Total outcomes}} imes 100
Substituting in our values:
ext{Percentage} = rac{7}{16} imes 100 = 43.75 \%
Thus, Alice wins at least one prize in 43.75% of the combinations.