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Favorable outcomes refer to the specific results that satisfy the condition we're interested in, in a probability experiment. Here, we are rolling two dice and are interested in the outcomes where their sum equals 6. Each possible pair that sums to 6 is a favorable outcome. Let's look at these pairs:

• (1,5)
• (2,4)
• (3,3)
• (4,2)
• (5,1)

These five pairs are the only combinations, with numbers from 1 to 6 on each die, that yield a total of 6 when added together. Therefore, there are 5 favorable outcomes in this scenario.

Total outcomes encompass all the possible results that can occur when an experiment is conducted. In the case of rolling two six-sided dice, each die has 6 possible faces. When working out the total number of outcomes, you multiply the possibilities for the first die with the possibilities for the second. Thus, there are:

• 6 possibilities from the first die
• 6 possibilities from the second die

This multiplication results in a total of 36 outcomes, because each of the 6 faces can pair with any of the 6 faces of the second die. Understanding the total number of outcomes is key when calculating probabilities, as it serves as the denominator in our probability formula.

The sum of two dice is simply the combined total of the numbers showing on each die after they are rolled. When calculating probability based on the sum of two dice, you're focusing on specific numerical results that can be obtained. For example, when interested in the sum being 6, you need to consider which pairs of numbers from the first and second die add up to 6. With six possible numbers on each die, the sums can vary from 2 (1+1) to 12 (6+6). In our exercise, the sum of 6 is created by the combinations (1,5), (2,4), (3,3), (4,2), and (5,1). Each pairing aligns with our favorable outcomes, making these combinations critical in determining the probability of rolling a sum of 6. The clarity in knowing which pairs result in the desired sum facilitates more straightforward calculation of probabilities.