There are a total of 16 possible outcomes when two eight-sided dice are thrown. Since one of the dice shows a four, there are only 8 possible outcomes left. These outcomes are: (4,1), (4,2), (4,3), (4,5), (4,6), (4,7), (4,8). Out of these 8 possible outcomes, only one outcome has a sum of eight, namely (4,4). Therefore, the probability that the sum on the two dice is eight, given that one of the dice shows a four, is 1/8.
