Final answer:
The answer is D. G and H are independent events because the probability of G occurring is the same regardless of whether H has occurred, defining them as independent in probability theory.
Step-by-step explanation:
If P(G|H) = P(G), this indicates that the likelihood of event G occurring is the same whether we know event H has occurred or not. In probability theory, this condition is the definition of independence between two events. Therefore, the correct answer to the question, "If P(G|H) = P(G), then which of the following is correct?" is:
D. G and H are independent events.
The other options provided do not accurately describe the relationship between events G and H when P(G|H) equals P(G).