Final answer:
The probability of selecting the "mathematics" volume when choosing two volumes at random from an eight-volume encyclopedia is 1/2 or 4/8. We consider the two cases where the "mathematics" volume is picked first or second and find a total of 14 successful outcomes out of 28 possible outcomes.
Step-by-step explanation:
The question requires calculating the probability of selecting the "mathematics" volume when two volumes are chosen at random from an eight-volume encyclopedia. To find this probability, we can consider the event of choosing the mathematics volume as a success. The probability of choosing the mathematics volume as one of the two volumes picked can be calculated as follows:
There are 8 volumes in total, and only 1 is the "mathematics" volume, so the probability of selecting the "mathematics" volume first is 1/8. However, since we are choosing two volumes, we must also consider the cases where the "mathematics" volume is picked second. Therefore, the total number of ways to choose 2 volumes out of 8 is 8 choose 2, which is equal to 28.
If the "mathematics" volume is picked first, there are 7 volumes left for the second pick, so there are 7 possible outcomes. If the "mathematics" volume is not picked first, there are 7 remaining picks and only 1 way to pick the "mathematics" volume second. So, the total number of successful outcomes is 7 (first pick) plus 7 (second pick), which equals 14. Thus, the probability of choosing the "mathematics" volume is:
P(mathematics volume) = Number of successful outcomes / Total number of outcomes = 14 / 28 = 1/2 or 4/8.
Therefore, the correct answer is (d) 4/8, indicating that the probability of selecting the mathematics volume in two random picks is 1/2.