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

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution