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 □ possible outcomes from rolling two dice. (simplify your answer. type an integer or a fraction.)

Explanation:

For the number of possible outcomes when rolling two dice:

Step1: Determine outcomes for one die

A single die has 6 possible outcomes (1, 2, 3, 4, 5, 6).

Step2: Calculate total outcomes for two dice

When rolling two dice, the total number of possible outcomes is the product of the number of outcomes for each die. So we use the multiplication principle: if one event has \( n_1 \) outcomes and another independent event has \( n_2 \) outcomes, the total number of outcomes for both events is \( n_1\times n_2 \). Here, \( n_1 = 6 \) (for the first die) and \( n_2 = 6 \) (for the second die), so the total number of outcomes is \( 6\times6 = 36 \).

Step1: Find total possible outcomes

As calculated above, when rolling two dice, the total number of possible outcomes is \( 6\times6 = 36 \).

Step2: Find favorable outcomes (sum = 3)

We need to find the pairs of numbers \((x, y)\) where \( x \) is the result of the first die, \( y \) is the result of the second die, and \( x + y=3 \). The possible pairs are \((1, 2)\) and \((2, 1)\). So there are 2 favorable outcomes.

Step3: Calculate probability

The probability \( P \) of an event is given by the formula \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \). Substituting the values, we get \( P = \frac{2}{36}=\frac{1}{18} \).

Answer:

36

For the probability of getting a sum of 3 when rolling two dice: