For two events A and B, the probability that A occurs is 0.6, the probability that B occurs is 0.5, and the probability that both occur is 0.3. Given that B occurred, what is the probability that A also occurred?
My work: $P(A|B) = \frac{P(A\cap B)}{P(B)} = \frac{0.3}{0.5} = 0.6$ which matches the probability of A in the question? Did I do something wrong or is this just a coincidence?
Your answer is correct. To understand why it is that $P(A \mid B) = P(A)$ in this case, look up the definition of independent events at Wikipedia and think about how that relates to your specific problem.