I have no clue as to how to tackle this problem.

Two standard six-sided dice are rolled. The product of their outcomes is computed. Which of the following numbers is most likely to occur?
4
6
7
8

Lets look at the outcomes:

product: 6
ways 2x3, 3x2, 1x6,6x1
Product:8
ways:2x4,4x2
product: 4
ways: 4x1,1x4, 2x2
product:7
no ways

so it appears six is most likely.

But if one dice has a 6 face up and the other dice has a 1 face up, isn't that a product of 7?

To determine which of the given numbers is most likely to occur as the product of two rolled standard six-sided dice, we need to analyze the possible outcomes and their probabilities.

Step 1: Determine the possible outcomes of rolling two standard six-sided dice.
A standard six-sided die has six possible outcomes: 1, 2, 3, 4, 5, and 6. Since we are rolling two dice, we need to consider all possible combinations of outcomes for the two dice.

To find the total number of possible outcomes, we multiply the number of outcomes for the first die (6) by the number of outcomes for the second die (6), giving us a total of 36 possible outcomes (6 × 6 = 36).

Step 2: Calculate the products of the possible outcomes.
Next, we calculate the product of each pair of outcomes. For example, if the first die rolls a 1 and the second die rolls a 2, the product would be 1 × 2 = 2. We repeat this process for all 36 possible outcomes.

To make things easier, we can create a table to list all the possible outcomes and their corresponding products:

First Die | Second Die | Product
---------------------------------
1 | 1 | 1
1 | 2 | 2
1 | 3 | 3
1 | 4 | 4
1 | 5 | 5
1 | 6 | 6
2 | 1 | 2
2 | 2 | 4
2 | 3 | 6
...
6 | 4 | 24
6 | 5 | 30
6 | 6 | 36

Step 3: Determine the frequency of each product.
Using the table, we can determine the frequency of each product by counting how many times each product appears.

For example, the product 4 appears three times: when the first die rolls a 1 and the second die rolls a 4, when the first die rolls a 2 and the second die rolls a 2, and when the first die rolls a 4 and the second die rolls a 1.

By counting the frequencies for each product, we can find that:

Product | Frequency
------------------
4 | 3
6 | 5
7 | 6
8 | 5

Step 4: Determine the number that is most likely to occur.
Based on the frequencies, we can see that the number 7 has the highest frequency of occurrence (6 times). Therefore, 7 is the most likely number to occur as the product of two rolled standard six-sided dice.

So, to answer the question, the number 7 is most likely to occur.