An archer has a 30% chance of hitting the bull's eye on the target.

a. What is the complement to this event and what is its probability?

b. What is the probability that he hits the target with only one of two arrows shot?

c. What is the probability that both arrows hit the bull's eye?

d. If the archer becomes more confident after a successful shot (i.e. the probability of the second shot hitting the target rises to 50%) and less confident (probability falls to 20%) after a miss, how would this affect the answers to parts (b) and (c)?

e. Explain the importance of the assumption of independence for the answers to (b) and (c)