Fighting probability of fallow deer bucks. In Aggressive Behavior (Jan./Feb. 2007), zoologists investigated the likelihood of fallow deer bucks fighting during the mating season. During the observation period, the researchers recorded 205 encounters between two bucks. Of these, 167 involved one buck clearly initiating the encounter with the other. In these 167 initiated encounters, the zoologists kept track of whether or not a physical contact fight occurred and whether the initiator ultimately won or lost the encounter.

(The buck that is driven away by the other is considered the loser.) A summary of the 167 initiated encounters is provided in the table on p. 171. Suppose we select one of these 167 encounters and note the outcome (fight status and winner).

a. What is the probability that a fight occurs and the initiator wins?

b. What is the probability that no fight occurs?

c. What is the probability that there is no clear winner?

d. What is the probability that a fight occurs or the initiator loses?

e. Are the events “No clear winner” and “Initiator loses”

mutually exclusive?

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