Suppose that here are three strikers in a football team: Lionel, Kylian, and Luka. The probabilities that they score a penalty kick are $, 82, and s3, respectively. When a penalty kick is awarded to this team, the manager decides that Lionel takes the kick with probability k, Kylian with probability k2, and Luka with probability k3. We assume S1, S2, S3, k1, k2, k3 (0, 1), and k+k + k3 = 1. (a) Find the probability that the kick is successful. (b) Find the probability that the kick was taken by Lionel, given that the kick is suc- cessful. (c) Are the events A = {the kick is taken by Lionel} and B = {the kick is taken by Kylian} independent? Explain why mathematically (not just verbally). (d) Under what condition are the events A = {the kick is taken by Lionel} and C {the kick is successful} independent? Explain. =