MATH 218
FINAL EXAM
Fall 1999
I
NSTRUCTIONS
. Every numerical answer should be simplified to a fraction
or a decimal, unless otherwise stated. You must show your work and justify
your methods to obtain full credit. Use the continuity correction wherever
it is appropriate unless otherwise instructed. If you can’t do one part of a
problem but need that answer later, guess an answer and use that guess for
the later part. The exam is worth a total of 200 points.
Problem
1
.
(15 points) A certain investor is interested in a group of 30 stocks.
Among these stocks are 17 stocks traded at the New York Stock Exchange
(NYSE) and 13 stocks traded at the American Stock Exchange (Amex): Among
the NYSE stocks, the prices of 12 stocks are up since the previous trading day
and the prices of 5 stocks are down. Among the Amex stocks, the prices of
7 stocks are up since the previous trading day and the prices of 6 stocks are
down. When appropriate, you may leave your answer in terms of factorials.
(a) Suppose one stock is selected at random. Let
A
represent the event that
a stock traded on the NYSE is chosen, and let
B
represent the event
that a stock whose price has risen is chosen. Find
P
(
A
)
and
P
(
A

B
)
.
(b) Are
A
and
B
independent? Show your work.
(c) The investor needs to read a report on each of the Amex stocks whose
price is up since the previous trading day, and must choose the order in
which to read them. How many ways are there for the investor to do
this? Show your work.
(d) How many ways can the investor choose a group of 5 different stocks
to buy from the group of 13 Amex stocks?
(e) Suppose that the investor wants to invest in some of the 13 Amex
stocks. How many ways can the investor choose a group of 3 Amex
stocks that are up and a group of 2 Amex stocks that are down?
Problem
2
.
(15 points) USC students are either in the college of Letters, Arts
and Sciences (LAS), the graduate school (GS) or the professional schools
(PS). The percentage of students in each group that support Al Gore for pres
ident in the 2000 election are as follows: LAS, 30%; GS, 40%; PS, 20%.
There are currently 12000 students enrolled in LAS, 6000 students enrolled
in the graduate school, and 9000 students enrolled in the professional schools.
(a) What is the probability that a student chosen at random from the USC
student body is enrolled in one of the professional schools?
(b) What is the probability that a student chosen at random from the USC
student body will support Al Gore in the 2000 presidential election?
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 Spring '06
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