Zoologists investigated the likelihood of fallow deer bucks fighting during the mating season. during a 270-hour observation period, the researchers recorded 205 encounters between two bucks. of these, 166 involved one buck clearly initiating the encounter with the other. in these 166 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.) suppose we select one of these 175 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 no clear initiator totals
wins winner loses
fight 28 28 12 68
no fight 84 12 11 107
totals 112 40 23 175