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

To find the percentage of combinations where Alice wins at least one prize, we can start by calculating the total possible combinations of winners.

1. Total Combinations: There are 4 candidates for Mathematics (Alice, Ben, Emma, Paddy) and 4 candidates for English (Alice, Claire, Gabi, Simon). Hence, the total number of combinations is:

   $ext{Total Combinations} = 4 imes 4 = 16$

2. Combinations Involving Alice: Now, we need to calculate how many combinations have Alice winning at least one prize. This can happen in two cases:

   • Case 1: Alice wins the Mathematics prize
   • Case 2: Alice wins the English prize

   Let's consider these cases:

   • If Alice wins Mathematics, there are 4 choices for English (Alice, Claire, Gabi, Simon). Thus, there are 4 combinations for this case.
   • If Alice wins English, there are 3 choices for Mathematics (Ben, Emma, Paddy). This gives us 3 combinations for the second case.

3. Total Favorable Outcomes: To avoid double counting the combination where Alice wins both prizes, we can summarize:

   • From Case 1: Alice wins Mathematics → 4 combinations
   • From Case 2: Alice wins English → 3 combinations
   • Both prizes: 1 combination (Alice in both)

   Therefore, the total combinations where Alice wins at least one prize is:

   $ext{Favorable Outcomes} = 4 + 3 - 1 = 6$

4. Calculating the Percentage: Finally, the percentage of combinations where Alice wins at least one prize is calculated as follows:

   ext{Percentage} = rac{ ext{Favorable Outcomes}}{ ext{Total Combinations}} imes 100 = \frac{6}{16} imes 100 = 37.5\%

Thus, the answer is:

Alice wins at least one prize in 37.5% of the combinations.