Final answer:
The probability of spinning a total of 8 on two fair four-sided spinners is 1/16, as there is only one combination (4,4) that gives this sum out of the 16 possible outcomes.
Step-by-step explanation:
The question asks to determine the probability of spinning a total of 8 when spinning two fair four-sided spinners. To find this probability, we first establish the sample space of the combined outcomes of both spinners. Having four sides on each spinner, we can enumerate the possibilities for the sums, similar to the method of listing outcomes for rolling dice or flipping coins.
For two four-sided spiners, each spinner can land on numbers 1 through 4, making the possible outcomes for the sum range from 2 (1+1) to 8 (4+4). We can visualize this by creating a grid that lists all combinations. In this grid, there would be only one combination yielding the sum of 8, which is (4,4). Since there are a total of 16 possible outcomes (4 sides on the first spinner x 4 sides on the second spinner), the probability of obtaining a sum of 8 is 1 out of 16 outcomes.
Therefore, the probability of the combined result being 8 is 1/16. We express this as a fraction in its simplest form, which it already is.
To concretize our understanding, probability problems often round answers to a certain number of decimal places. However, in this case, since our final answer is already expressed as a simple fraction, such rounding is not required or applicable.