What is the probability of getting a sum 9 from two throws of a dice?

When two dice are thrown, each die's outcome is independent, so every ordered pair of face values (first die, second die) is equally likely. The probability of any event is the number of ordered pairs satisfying the event divided by the total number of ordered pairs.

1. Since each die has 6 faces and the two throws are independent, the total number of equally likely ordered outcomes is 6 × 6 = 36.

2. List every ordered pair of dice values whose sum is 9: (3, 6), (4, 5), (5, 4), and (6, 3) — 4 such pairs.

3. Probability = (favourable outcomes) / (total outcomes) = 4/36, which simplifies to 1/9.

As a check, note that the sums produced by two dice are symmetric about 7: the number of pairs summing to 9 must equal the number summing to 5 (namely (1, 4), (2, 3), (3, 2), (4, 1) — also 4 pairs), confirming that 4 is indeed the correct count of favourable outcomes.