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The problem in the image asks to find the probability that the sum of rolling two dice will be less than 3 or greater than 6.

### Step 1: Understand the total number of possible outcomes
When rolling two dice, each die has 6 faces, so the total number of possible outcomes is:

\[
6 \times 6 = 36
\]

### Step 2: Identify the favorable outcomes
- **Sum less than 3:** The smallest possible sum is 2, which can only be achieved by rolling a 1 on both dice (1,1). So, there is only **1 favorable outcome** for the sum to be less than 3.
  
- **Sum greater than 6:** We need to find all the outcomes where the sum is greater than 6. These sums can be:
  - 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes
  - 8: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes
  - 9: (3,6), (4,5), (5,4), (6,3) → 4 outcomes
  - 10: (4,6), (5,5), (6,4) → 3 outcomes
  - 11: (5,6), (6,5) → 2 outcomes
  - 12: (6,6) → 1 outcome
  
So, the number of favorable outcomes for a sum greater than 6 is:

\[
6 + 5 + 4 + 3 + 2 + 1 = 21
\]

### Step 3: Add the favorable outcomes
The favorable outcomes for the event "less than 3 or greater than 6" are:
\[
1 \text{ (for less than 3)} + 21 \text{ (for greater than 6)} = 22
\]

### Step 4: Calculate the probability
The probability is the ratio of favorable outcomes to total outcomes:

\[
\frac{22}{36} = \frac{11}{18}
\]

### Final Answer: 
The probability that the sum will be less than 3 or greater than 6 is:

\[
\frac{11}{18}
\]

Would you like further details or have any other questions?

Here are some related questions:
1. What is the probability that the sum of the dice will be exactly 7?
2. How many outcomes result in a sum less than or equal to 4?
3. What is the probability of rolling a sum of 9?
4. How would the probability change if the dice were biased?
5. What is the probability of rolling a sum between 4 and 10?

**Tip:** In problems involving dice, always list all possible outcomes for the sums you are interested in to avoid missing any possibilities!

For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be less than 3 or greater than 6.

Discover how to calculate the probability of rolling a sum less than 3 or greater than 6 using two dice. This detailed solution explains the steps, covering key probability concepts and formulas. Suitable for students in Grades 6-8.

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