A pair of fair six-sided dice are rolled. What is the probability of rolling a sum less than 4?

To determine the probability of rolling a sum less than 4 with two fair six-sided dice, let's follow these steps:

### Step 1: Possible outcomes
Each die has 6 faces, so there are a total of:

\[
6 \times 6 = 36 \text{ possible outcomes}.
\]

### Step 2: Identify favorable outcomes
The sum of two dice can be less than 4 if the results of the dice sum to 2 or 3. Let's list the favorable outcomes:

- Sum of 2: (1, 1)
- Sum of 3: (1, 2), (2, 1)

Thus, the favorable outcomes are:

\[
(1, 1), (1, 2), (2, 1)
\]

There are 3 favorable outcomes.

### Step 3: Calculate the probability
The probability of an event is the ratio of favorable outcomes to the total possible outcomes. Therefore, the probability of rolling a sum less than 4 is:

\[
\frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{3}{36} = \frac{1}{12}.
\]

Thus, the probability of rolling a sum less than 4 is \(\frac{1}{12}\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the probability of rolling a sum greater than 10 with two dice?
2. What is the probability of rolling a sum of exactly 7 with two dice?
3. How many outcomes result in a sum of 5 when rolling two six-sided dice?
4. What is the probability of rolling doubles with two dice?
5. If one die is fixed to show a 3, what is the probability of rolling a total less than 8?

**Tip**: When solving probability problems, it helps to carefully list all possible outcomes and systematically identify favorable ones.

Explore how to calculate the probability of rolling a sum less than 4 with two fair six-sided dice. This problem uses basic probability theory and combinatorics to find the solution, with a step-by-step breakdown. Ideal for students in Grades 6-8.

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