Let's analyze the given information and statements one by one.

1. Given: \(P(A) = P(A|B) = 0.25\) and \(P(B|A) = 0.5\)
2. To check if events A and B are independent, we need to verify if \(P(A|B) = P(A)\) and \(P(B|A) = P(B)\).
   • Since \(P(A) = P(A|B) = 0.25\), this condition for independence holds.
   • We also know \(P(B|A) = 0.5\).

Let's find \(P(B)\) using the formula for conditional probability:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

Substitute the known values:

\(0.5 = \frac{P(A \cap B)}{0.25} \Rightarrow P(A \cap B) = 0.5 \times 0.25 = 0.125\)

Now, using the formula \(P(A \cap B) = P(A) P(B)\) for independent events:

\(P(B) = \frac{P(A \cap B)}{P(A)} = \frac{0.125}{0.25} = 0.5\)

Thus, the events A and B are independent. So, statement I is correct.

Now, let's verify statement II.

Using the formula for the complement of a union:

\(P(A^c \cup B^c) = 1 - P(A \cap B)\)

Substituting the value of \(P(A \cap B) = 0.125\):

\(P(A^c \cup B^c) = 1 - 0.125 = 0.875\)

Therefore, statement II is correct.

Lastly, let's evaluate statement III.

Using De Morgan's law: \(P(A^c \cap B^c) = 1 - P(A \cup B)\)

We can use the property of probabilities:

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

Substitute the known values:

\(P(A \cup B) = 0.25 + 0.5 - 0.125 = 0.625\)

Therefore:

\(P(A^c \cap B^c) = 1 - 0.625 = 0.375\)

Statement III is also correct.

Hence, the correct answer is: I, II and III.