Consider the University of Newcastle (UON) service area (i.e., the area within which the attending student population resides) as consisting solely of the following three locations: • Central Coast (CC) • Hunter excluding Newcastle (HEN) • Lake Macquarie and Newcastle (LMN) According to the Australian Bureau of Statistics: • the relative proportions of residents in each of these three locations is 34.6% in CC, 27.0% in HEN and 38.4% in LMN; and • 14.6% of residents in the CC area were born overseas • 8.4% of residents in the HEN area were born overseas • 11.7% of residents in the LMN area were born overseas. Let B be the event that a resident was born overseas, CC be the event that a resident lives in the Central Coast, HEN be the event that a resident lives in the Hunter excluding Newcastle area, and LMN be the event that a resident lives in the Lake Macquarie and Newcastle area.

a) Construct a tree diagram that summarises the given probability information. It should identify the probabilities of residing in each of three locations and the probabilities of having been born overseas, or not, for each location.

b) What is the probability that a randomly selected resident in the UON service area is a resident of the Central Coast and was born overseas?

c) What is the probability that a randomly selected resident in the UON service area was born overseas?

d) Are the events B and CC independent? Provide rationale for your decision.

e) If a randomly selected resident in the UON service area was born overseas, what is the probability that he or she is a resident of the Hunter excluding Newcastle area?

f) In part (c), you found the probability that a randomly selected resident in the UON service area was born overseas. Can you infer that this probability is the same as the probability that a UON student was born overseas? Justify your response