Question

Think About the Process  A single number cube is rolled twice. The 36​ equally-likely outcomes are shown to the right. What is the first step in finding the probability of getting two numbers whose sum is 4​? Find the probability of getting two numbers whose sum is 4.
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Part 1
What is the first step in finding the probability of getting two numbers whose sum is 4​?
A.
Divide 4 by 6.
B.
Divide 4 by 36.
C.
Find the number of combinations that will give a sum of 4 using the numbers 1 through 6.
D.
Find the number of combinations that will give a sum of 4 using the numbers 1 through 36.
What is the first step in finding the probability of getting two numbers whose sum is 4?

Answer 1

To find the probability of getting two numbers whose sum is 4 when rolling a single number cube (die) twice, the first step is to identify the combinations that can result in that sum. Thus, the correct answer is:

**C. Find the number of combinations that will give a sum of 4 using the numbers 1 through 6.**

Next, let's calculate the probability:

1. **Identify the combinations that yield a sum of 4**:
- (1, 3)
- (2, 2)
- (3, 1)

There are a total of **3 combinations** that give a sum of 4.

2. **Calculate the total number of outcomes** when rolling the die twice:
- There are 6 outcomes for the first roll and 6 outcomes for the second roll, so there are \(6 \times 6 = 36\) total possible outcomes.

3. **Calculate the probability**:
\[
\text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{3}{36} = \frac{1}{12}
\]

Therefore, the probability of getting two numbers whose sum is 4 is \(\frac{1}{12}\).