A box contains 4 red balls and 4 black balls of identical size and weight. One ball is drawn at random from the box and, simultaneously, a fair coin is tossed. Considering this combined experiment, answer the following questions:
a. (i) Write the complete sample space for the combined experiment.
b. (ii) Let event A be ‘the ball drawn is red or the coin shows head’. Determine P(A) and decide whether A is a sure, impossible or neither type of event. Give justification.
c. (iii) Let event B be ‘the ball drawn is blue’. Calculate P(B) and classify the event type. Give reason.
d. (iv) Show that the complement of an impossible event is a sure event by using event B and its complement in this situation. Provide a brief explanation linking their probabilities.