All the computations referred here relates to k=5.
In general terms, answer to (c) is (0.81)k
Answer to (d) is 2*(0.9)k- (0.81)k
If A= event (a), B=event (b), then event (c) = P(A)*P(B) , event (d) = \(\displaystyle P(A) \cup P(B)= P(A) + P(B) -P(A) \cap P(B)\)