The question asks for the number of ways two six-sided dice (one red and one green) can be rolled so that their total is less than 7. Here's how we solve this step by step systematically:

Step 1: Possible Totals Less Than 7

The possible sums less than 7 are:

• $2, 3, 4, 5, 6$.

Step 2: Systematic Listing

We list all possible dice combinations for each sum where the first die represents the red die, and the second die represents the green die.

• Sum = 2:
  $(1, 1)$ → 1 way.

• Sum = 3:
  $(1, 2), (2, 1)$ → 2 ways.

• Sum = 4:
  $(1, 3), (2, 2), (3, 1)$ → 3 ways.

• Sum = 5:
  $(1, 4), (2, 3), (3, 2), (4, 1)$ → 4 ways.

• Sum = 6:
  $(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)$ → 5 ways.

Step 3: Total Number of Ways

Add up the number of ways for each sum: $1 + 2 + 3 + 4 + 5 = 15.$

Thus, there are 15 ways to roll a total less than 7.

Would you like a breakdown of probabilities or any additional details? Let me know! 😊

Here are 5 related questions for practice:

1. How many ways can you roll exactly a sum of 7 with two dice?
2. What is the probability of rolling a sum less than 5?
3. How many total outcomes are possible when rolling two dice?
4. If the dice were eight-sided instead of six-sided, how many outcomes would give a sum less than 7?
5. How can you determine the probability of rolling a sum greater than or equal to 10?

Tip: Always double-check your systematic listings to ensure no combinations are missed or repeated.