Fighting probability of fallow deer bucks. Refer to the Aggressive Behavior (Jan./Feb. 2007) study of fallow deer bucks fighting during the mating season, presented in Exercise 3.61 (p. 170). Recall that researchers recorded 167 encounters between two bucks, one of which clearly initiated the encounter with the other. A summary of the fight status of the initiated encounters is provided in the accompanying table. Suppose we select 1 of these 167 encounters and note the outcome (fight status and winner).

a. Given that a fight occurs, what is the probability that the initiator wins?

b. Given no fight, what is the probability that the initiator wins?

c. Are the events “no fight” and “initiator wins”

independent?

Initiator Wins No Clear Winner Initiator Loses Totals Fight 26 23 15 64 No Fight 80 12 11 103 Totals 106 35 26 167