Final answer:
The probability of getting either a sum of 8 or at least one 6 when rolling a pair of dice is 14/36, which simplifies to 7/18.
Step-by-step explanation:
Calculating Probability with Dice
To find the probability of getting either a sum of 8 or at least one 6 when rolling a pair of dice, we must first determine the sample space and the desired events.
The sample space when rolling two six-sided dice is 36, since each die has 6 faces and the rolls are independent (6 x 6 = 36). To get a sum of 8, the following pairs are possible: (2,6), (3,5), (4,4), (5,3), (6,2). That's 5 outcomes. For rolling at least one 6, we get (6,1), (6,2), (6,3), (6,4), (6,5), (6,6), in addition to the combinations with 6 as the first number, which have been already counted, which adds 5 more unique outcomes. So, there are 10 outcomes with at least one 6.
However, we must also consider that the outcome (2,6) and (6,2) have been counted twice. Therefore, we subtract 1 from the total count, making it 14 unique favorable outcomes for the two events combined. So, the probability of getting either a sum of 8 or at least one 6 is 14/36, which can be simplified to 7/18.
Remember that in probability theory, the likelihood of an event is often expressed as a fraction or decimal, and understanding these basics will support you in solving various probability problems.