Question

a pair of dice is rolled. what is the probability of getting a sum of 3? how many possible outcomes are there from rolling two dice? there are 36 possible outcomes from rolling two dice. (simplify your answer. type an integer or a fraction.) how many ways can two dice be rolled such that their sum is 3? there is/are □ way(s) two dice can be rolled such that their sum is 3. (simplify your answer. type an integer or a fraction.)

Explanation:

For the number of ways to get a sum of 3:

Step1: List possible dice rolls

We consider the outcomes of two dice, where the first die is \(x\) and the second is \(y\), and we need \(x + y=3\). The possible positive integer solutions (since dice show 1 - 6) are when \(x = 1,y = 2\) and \(x = 2,y = 1\).

Step2: Count the solutions

We have 2 distinct ordered pairs: \((1,2)\) and \((2,1)\).

Step1: Recall probability formula

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\).

Step2: Identify values

We know the total number of possible outcomes when rolling two dice is 36 (from the given information), and the number of favorable outcomes (sum = 3) is 2 (from the previous calculation).

Step3: Calculate probability

Substitute into the formula: \(P=\frac{2}{36}=\frac{1}{18}\).

Answer:

2

For the probability of getting a sum of 3: