Students are asked to choose one subject from Option A and one subject from Option B - OCR - GCSE Maths - Question 12 - 2020 - Paper 6

Now, check for any subjects that have the same first letters. From Option A, we have:

• Economics (E)
• Geography (G)
• History (H)
• Media Studies (M)

From Option B, we have:

• Art (A)
• Drama (D)
• Engineering (E)
• German (G)
• Graphics (G)
• Music (M)
• PE (P)

Matching pairs can be identified as:

• Economics (E) and Engineering (E)
• Geography (G) and German (G)
• Media Studies (M) and Music (M)

In total, there are 3 favorable outcomes.

Finally, calculate the probability by dividing the number of favorable outcomes by the total number of combinations:

$Probability = \frac{Number\, of\, Favorable\, Outcomes}{Total\, Combinations} = \frac{3}{24} = \frac{1}{8}$

Thus, the probability that both subjects have the same first letter is ( \frac{1}{8} ).