Final answer:
The probability of selecting a two-member subset from the given set S that satisfies the equation {K－M} = 2 is 8/45.
Step-by-step explanation:
To find the probability that the member of the subset will satisfy the equation {K－M} = 2, we need to determine the number of favorable outcomes and the total number of possible outcomes.
There are 10 total numbers in the set S. For the member of the subset to satisfy the equation {K－M} = 2, K and M must be two numbers that differ by 2.
We can choose 2 numbers that differ by 2 in the following ways: (0, 2), (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8), (7, 9). So, there are 8 favorable outcomes.
Therefore, the probability is the number of favorable outcomes divided by the total number of possible outcomes, which is 8/45.