Question

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, 172 involved one buck clearly initiating the encounter with the other. In these 172 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 172 encounters and note the outcome​ (fight status and​ winner).

Initiator Wins No Clear Winner Initiator Loses Totals

Fight 29 20 16 65

No Fight 84 12 11 107

Totals 113 32 27 172

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?

Answer 1

	win	no clear	loss	total
fight	29	20	16	65
no	84	12	11	107
total	113	32	27	172

a)  
P(fight occurs and wins) = 29/172=   0.168604651
  
b)  
P(no fight) = 107/172=   0.622093023
  
c) P(no clear winner) = 32/172=   0.186046512
  
d) P(fight occur or iniator losses) = (29+20+16+11)/172=   0.441860465
  
e)

the events​ "no clear​ winner" and​ "initiator loses" are mutually​ exclusive

because either there will be no clear winner or iniator will lose.that cannot happen together at same time