(a) Define the term “independent events.”
(b) State the multiplication theorem relating the probability of the intersection of two independent events.
(c) A fair die is thrown once and a fair coin is tossed once. Let D be the event “the die shows 4” and C be the event “the coin shows Head.”
(i) Show that D and C are independent.
(ii) Verify the multiplication theorem numerically for these two events.