Questions: A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 6. The probability of getting two numbers whose sum is 6 is . (Type an integer or a simplified fraction.)

$A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 6. The probability of getting two numbers whose sum is 6 is . (Type an integer or a simplified fraction.)$

Transcript text: A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 6. The probability of getting two numbers whose sum is 6 is $\square$ . (Type an integer or a simplified fraction.)

Solution

Solution Steps

Step 1: Enumerate all possible outcomes

Since the die has 6 sides and is rolled twice, there are $6^2 = 36$ equally likely outcomes.

Step 2: Identify outcomes that meet the condition

We identify all pairs $(i, j)$ where $i$ and $j$ are the outcomes of the first and second rolls, respectively, and they meet the condition: i + j == 6. This gives us a total of 5 favorable outcomes.

Step 3: Calculate the probability

The probability is the ratio of the number of favorable outcomes to the total number of possible outcomes, $P = \frac{5}{36} = 0.14$.