Final answer:
To find the probability of a specific sum when tossing two 6-sided dice, calculate the total number of outcomes (36) and then count the favorable outcomes for that sum. Divide the number of favorable outcomes by the total outcomes to get the probability as a fraction.
Step-by-step explanation:
To compute the probability that the sum of the pips on the upward faces of two regular 6-sided dice is a specific number, we first identify the total number of possible outcomes when two dice are rolled. Since each die has 6 sides, the total sample space consists of 6 x 6, which equals 36 possible combinations.
Next, we count the number of outcomes that result in the desired sum. For example, if we want the sum to be 7, the following pairs will yield that sum: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1), resulting in 6 such pairs. Therefore, the probability of rolling a sum of 7 is 6/36, which simplifies to 1/6.
The process would be similar for other sums, with the number of favorable outcomes varying depending on the sum in question.
Probability, sample space, and the product rule are important concepts in solving these types of problems.