A coin is tossed once and, independently, a fair die is rolled once.
a. (i) Calculate the probability of the event A: "The coin shows a head and the die shows an even number".
b. (ii) Calculate the probability of the event B: "The coin shows a tail or the die shows a multiple of 3".
c. (iii) Without converting the probabilities to decimals, compare P(A) and P(B) by expressing both probabilities as fractions with a common denominator.
d. (iv) State which event is more likely and by how much their probabilities differ.