A fair six–faced die is rolled once and, at the same instant, a fair coin is tossed once. Let
A = "the die shows an even number" and B = "the coin shows a head".
a. (i) Explain, without calculation, whether events A and B are independent. Give a brief reason.
b. (ii) Calculate the probability that both A and B occur together in the single combined trial.
c. (iii) If the outcome of the coin is known to be a head, does the probability of A change? Give a clear justification for your answer based on the definition of independence.