Question

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in table #4.3.3 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Table #4.3.3: Dolphin Activity Activity Period Morning Noon Afternoon Evening Total Travel 6 6 14 13 39 Feed 28 4 0 56 88 Social 38 5 9 10 62 Total 72 15 23 79 189 a.) What is the probability that a dolphin group is partaking in travel? b.) What is the probability that a dolphin group is around in the morning? c.) What is the probability that a dolphin group is partaking in travel given that it is morning? d.) What is the probability that a dolphin group is around in the morning given that it is partaking in socializing? e.) What is the probability that a dolphin group is around in the afternoon given that it is partaking in feeding? f.) What is the probability that a dolphin group is around in the afternoon and is partaking in feeding? g.) What is the probability that a dolphin group is around in the afternoon or is partaking in feeding? h.) Are the events dolphin group around in the afternoon and dolphin group feeding mutually exclusive events? Why or why not? i.) Are the events dolphin group around in the morning and dolphin group partaking in travel independent events? Why or why not?

Answer 1

from above :

	morning	noon	afternoon	evening	total
travel	6	6	14	13	39
feed	28	4	0	56	88
social	38	5	9	10	62
total	72	15	23	79	189

a)

probability that a dolphin group is partaking in travel=39/189=0.2063

b)

probability that a dolphin group is around in the morning=72/189=0.3810

c)

probability that a dolphin group is partaking in travel given that it is morning=6/72=0.0833

d)

probability that a dolphin group is around in the morning given that it is partaking in socializing

=38/62=0.6129

e)

probability that a dolphin group is around in the afternoon given that it is partaking in feeding

=0/88=0

f)

probability that a dolphin group is around in the afternoon and is partaking in feeding

=0/189 =0

g)

probability that a dolphin group is around in the afternoon or is partaking in feeding

=(88+23-0)/189=0.5873

h)

Yes as they contain no common items they are mutually exclusive events

i)

No as probability that a dolphin group is partaking in travel given that it is morning is not equal to probability of travel ; tehrefore event are not independent