Final answer:
The probability of selecting the "mathematics" volume when randomly choosing two out of eight volumes is 1/4 or 0.25. This is calculated by dividing the 7 favorable ways to pair the "mathematics" volume with another volume by the 28 total possible outcomes when picking two volumes.
Step-by-step explanation:
The question asks for the probability of selecting the "mathematics" volume when choosing two volumes at random from an eight-volume encyclopedia set. To find this, we can use the concept of sample space and event probability. Since we are selecting two volumes and want one of them to be the "mathematics" volume, there are several combinations to consider, but we will streamline this by focusing on the key fact: the desired outcome includes the "mathematics" volume regardless of the other volume chosen.
The total number of ways to choose two volumes out of eight is the combination of 8 items taken 2 at a time (8 choose 2), which is 8! / (2! * (8-2)!), resulting in 28 possible combinations. Since the "mathematics" volume must be one of the two books chosen, we look at how many different volumes can be paired with it. There are seven other volumes, so there are seven possible ways to pair the "mathematics" volume with any other volume.
The probability of choosing the "mathematics" volume is therefore 7 (favorable outcomes) divided by 28 (total possible outcomes), which simplifies to 1/4 or 0.25. Thus, there is a 25% chance that when choosing two volumes at random, one of them will be the "mathematics" volume.