Question

a number cube with sides labeled 1- 6 is rolled two times, and the sum of the numbers that end face up is calculated. what is the probability that the sum of the numbers is 3?
\\(\frac{1}{18}\\)
\\(\frac{1}{12}\\)
\\(\frac{1}{9}\\)
\\(\frac{1}{2}\\)

Explanation:

Step1: Find total possible outcomes

Each roll has 6 outcomes, so two rolls: $6 \times 6 = 36$ total outcomes.

Step2: Identify favorable outcomes

Pairs summing to 3: (1,2) and (2,1) → 2 favorable outcomes.

Step3: Calculate probability

Probability = $\frac{\text{favorable}}{\text{total}} = \frac{2}{36} = \frac{1}{18}$.

Answer:

$\frac{1}{18}$