A fair six–faced die is thrown once and a fair coin is tossed simultaneously. Let
E be the event “the die shows an even number” and F be the event “the coin shows Heads.”
a. (i) Calculate P(E), P(F) and P(E∩F).
b. (ii) Decide whether the events E and F are independent. Show all working.
c. (iii) If the coin is replaced by another coin that shows Heads with probability 0.7 while the die remains fair, state with reason whether E and F would still be independent.