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.