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### 9-1: Experimental and Theoretical Probability

What is the probability of rolling numbers that add to 8 when rolling two standard number cubes? Use the chart to help you solve the problem.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline 1 & 1,1 & 2,1 & 3,1 & 4,1 & 5,1 & 6,1 \\
\hline 2 & 1,2 & 2,2 & 3,2 & 4,2 & 5,2 & 6,2 \\
\hline 3 & 1,3 & 2,3 & 3,3 & 4,3 & 5,3 & 6,3 \\
\hline 4 & 1,4 & 2,4 & 3,4 & 4,4 & 5,4 & 6,4 \\
\hline 5 & 1,5 & 2,5 & 3,5 & 4,5 & 5,5 & 6,5 \\
\hline 6 & 1,6 & 2,6 & 3,6 & 4,6 & 5,6 & 6,6 \\
\hline
\end{tabular}

A. [tex]$\frac{5}{36}$[/tex]
B. [tex]$\frac{1}{6}$[/tex]
C. [tex]$\frac{7}{36}$[/tex]
D. [tex]$\frac{11}{26}$[/tex]



Answer :

GinnyAnswer
To determine the probability of rolling a sum of 8 with two standard number cubes (each numbered from 1 to 6), let's walk through the problem step by step.

### Step 1: Identify the possible outcomes
When rolling two standard number cubes, each cube has 6 faces. This means there are a total of [tex]\( 6 \times 6 = 36 \)[/tex] possible outcomes when rolling the two dice.

### Step 2: Identify the favorable outcomes
Next, we need to identify the combinations of dice rolls that add up to 8. We can systematically examine pairs of dice faces that sum to 8:

1. [tex]\( (2, 6) \)[/tex]
2. [tex]\( (3, 5) \)[/tex]
3. [tex]\( (4, 4) \)[/tex]
4. [tex]\( (5, 3) \)[/tex]
5. [tex]\( (6, 2) \)[/tex]

Each of these pairs represents a favorable outcome. We can see that there are 5 such pairs.

### Step 3: Calculate the probability
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes:

[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \][/tex]

Substituting in the numbers we have identified:

[tex]\[ \text{Probability} = \frac{5}{36} \][/tex]

So, the probability of rolling numbers that add to 8 when rolling two standard number cubes is [tex]\( \frac{5}{36} \)[/tex].

### Step 4: Choose the correct answer
Among the given choices:
A. [tex]\( \frac{5}{36} \)[/tex]
B. [tex]\( \frac{1}{6} \)[/tex]
C. [tex]\( \frac{7}{36} \)[/tex]
D. [tex]\( \frac{11}{26} \)[/tex]

The correct answer is:
A. [tex]\( \frac{5}{36} \)[/tex]

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