Researchers recorded 167 encounters between two fallow deer bucks during the mating season, where one of which clearly initiated the encounter with the other. A summary of the fight status of the initiated encounters is provided below. Questions Suppose we select 1 of these 167 encounters at random and note the outcome (fight status and winner). Question 4, Part a: (5 points) Given that a fight occurs, what is the probability that the initiator wins? Question 4, Part b: (5 points) Given no fight, what is the probability that the initiator wins? Question 4, Part c: (5 points) Are the events "no fight" and "initiator wins" independent? Give a mathematical reasoning in support of your