Two dice thrown together: What is the probability that neither die shows a 4 (i.e., the outcome on every die is not 4)?

Introduction / Context:
We seek the probability both dice avoid a particular face. With independence, multiply the single-die avoidance probability across the two dice.

Given Data / Assumptions:
Each die: P(not 4) = 5/6; two independent dice.

Concept / Approach:
P(neither shows 4) = (5/6) * (5/6) by independence.

Step-by-Step Solution:

Verification / Alternative check:
Complement: 1 − P(at least one 4) = 1 − [1 − (5/6)^2] = (5/6)^2 = 25/36.

Why Other Options Are Wrong:
2/3 or 1/3 reflect single-die logic or complement misapplied; 17/36 is off by arithmetic.

Common Pitfalls:
Using 1 − 2*(1/6) which double-counts the “both 4” case.

Final Answer:
25/36