Two fair dice are rolled. The probability that the SUM of the numbers showing is 7 is

1. Sample space when rolling 2 dice: $|S| = 6 \times 6 = 36$ equally-likely ordered pairs. 2. Event 'sum = 7': list pairs $(a, b)$ where $a + b = 7$: $(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)$ → 6 outcomes. 3. $P(\text{sum} = 7) = 6/36 = 1/6$. 4. Interesting: SUM 7 is the most likely sum (more pairs achieve it than any other sum from 2 to 12). 5. Option A gives $3/36$ outcomes (off by half). Option B is $4/36$. Option D would mean 18 outcomes (impossible). _Source: syllabus Mathematics, Ch 14, §14.2.2 + Example 2 (Two-dice events), p. 4 + p. 8._