Two fair dice are thrown. What is the probability that the absolute difference between the two numbers is 2 or 3?

Introduction / Context:
We count ordered pairs (a,b) with a,b ∈ {1,…,6} such that |a − b| ∈ {2,3}. Counting favorable outcomes directly is efficient for small dice problems.

Given Data / Assumptions:

• Sample space size = 36 equally likely ordered pairs.
• We need |a − b| = 2 or 3.

Concept / Approach:
Enumerate the pairs for |a − b| = 2 and for |a − b| = 3. Sum them, divide by 36.

Step-by-Step Solution:

Verification / Alternative check:
Symmetry around the main diagonal implies for each a there are at most two b values satisfying |a − b| = k; tabulation matches the counts above.

Why Other Options Are Wrong:
5/18 corresponds to only one of the difference values; 1/2 greatly overestimates the event; 3/11 is not tied to a 36-sized space.

Common Pitfalls:
Forgetting that outcomes are ordered, or double-counting/omitting symmetric pairs.

Final Answer:
7/18