ECON1202 – Quantitative Analysis for Business & Economics

© Copyright University of New South Wales 2022. All rights reserved. This copyright notice must not
be removed from this material.

WEEK 4 WORKSHOP: PROBABILITY

Question 1 [Past Test Question]
Draw a probability tree to solve this problem. A qualifying test for a professional organisation
was given at four locations. One thousand students sat for the test at each of locations A and
B and 500 students sat for the test at each of locations C and D. Seventy percent of those who
sat at location A passed the test. The percentages of students from locations B, C and D who
passed were 75%, 65% and 72% respectively. If one student is selected at random from those
who sat for the test,
(a) what is the probability that the selected student passed the test?

(b) if the selected student passed the test, what is the probability that the student sat at location
C?

Question 2 (HPW 8.6, Problem 19, p.410)
At a certain fitness center, the probability that a member regularly attends an aerobics class is !". If two members are randomly selected, find the probability that both attend the class
regularly. Assume independence.

Question 3 (HPW 8.1, Problem 8, p. 354)
In how many ways is it possible to answer a six-question multiple-choice examination if each
question has four choices (and one choice is selected for each question)?

Question 4
A television station must schedule four programs for a particular night and has to decide which
programs to show and the order in which they will run. The station has eight programs from
which to choose. How many possible schedules are there?

Question 5 (HPW 8.2, Problem 37, p. 366)
At a tourist attraction, two trams carry sightseers up a picturesque mountain. One tram can
accommodate seven people and the other eight. A busload of 18 tourists arrives, and both the
trams are at the bottom of the mountain. Obviously, only 15 tourists can initially go up the
mountain. In how many ways can the attendant load 15 tourists onto the two trams?

Question 6 (HPW 8.2, Problem 33, p. 366)
A committee has three male and five female members. In how many ways can a subcommittee
of four be selected if:

a) Exactly 4 females are to serve on it?
b) Exactly 3 males are to serve on it?
c) at least two females are to serve on it?

Question 7 [Past Exam Question]
Anton plans to invest in 6 stocks consisting of Australian and global shares. He wants the
number of Australian shares to be twice the number of global shares given the strong
performance of the Australian equity market. After doing some research, he has shortlisted 8
Australian shares and 4 global shares. How many ways can Anton create his desired portfolio?


ECON1202 – Quantitative Analysis for Business & Economics

© Copyright University of New South Wales 2022. All rights reserved. This copyright notice must not
be removed from this material.

Brief solutions
Q1. a) 0.712; b) 0.152
Q2. 1/16
Q3. 4096
Q4. 1680
Q5. 5,250,960
Q6. b) 5, b) 5, c) 65
Q7. 420


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