What is the probability of getting a sum 5 from two throws of a dice?

Concept: When two fair dice are thrown, each die has 6 equally likely faces, so together they produce 6 × 6 = 36 equally likely ordered outcomes. For any event, Probability = (Number of favorable outcomes) ÷ (Total number of outcomes).

Application: List every ordered outcome (first die, second die) whose sum is exactly 5, then count them:

1. The ordered pairs are (1, 4), (4, 1), (2, 3), and (3, 2).

2. That gives 4 favorable outcomes out of the 36 total equally likely outcomes.

3. Probability = 4/36.

4. Dividing numerator and denominator by their greatest common factor, 4, gives 4/36 = 1/9.

Cross-check: Listing the pairs by first-die value confirms no pair is missed or repeated: die 1 shows 1 → partner 4; shows 2 → partner 3; shows 3 → partner 2; shows 4 → partner 1; no other die-1 value pairs with a valid die-2 value (1–6) to sum to 5. So exactly 4 outcomes qualify, confirming the probability is 1/9.