Final answer:
The sample space for a spinner divided into eight congruent sectors is {1, 2, 3, 4, 5, 6, 7, 8}. The probability of the spinner stopping on a 3 is 1 out of 8, expressed as the ratio 1:8.
Step-by-step explanation:
The question revolves around finding the sample space and the probability of landing on a particular number (in this case, a 3) when a spinner divided into eight congruent sectors is spun once. Since the spinner is divided equally into eight sectors, each sector represents one of the possible outcomes, making the sample space {1, 2, 3, 4, 5, 6, 7, 8}. The probability of landing on a given number, such as 3, is determined by dividing the number of ways event '3' can occur by the total number of possible outcomes. Thus, the probability of spinning a 3 is 1/8. This is equivalent to the ratio of 1:8, which expresses the probability that the spinner will stop in a sector labeled 3.