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CEE 3770  Summer 2009
Homework 1 (due on 05/21)
1. (6 points) Let
E,F,G
be three events. Suppose that
U
=
E
∪
F
∪
G
. Find expressions for
the events that of
E,F,G
(a) only F occurs.
(b) both E and F occur, but not G.
(c) at least one event occurs.
(d) at least two events occur.
(e) all three events occur.
(f) none occur.
2. (6 points) A box contains 3 marbles (two red and one blue). Consider an experiment that
consists of taking one marble from the box, then replacing it in the box, and then drawing a
second marble from the box.
(a) What is the sample space?
(b) Is it SSS(Simple Sample Space)? If not, construct a simple sample space.
(c) Find the probability that at least one blue marble is chosen.
3. (6 points) Repeat the above when the second marble is drawn without replacing the ﬁrst
marble.
(a) What is the sample space?
(b) Is it SSS(Simple Sample Space)? If not, construct a simple sample space.
(c) Find the probability that at least one blue marble is chosen.
4. (6 points) On a surprise quiz with two questions, the ﬁrst question is multiple choice with
a,b,c and d (4 alternatives) while the second question is a true/false question. A student is
completely unprepared for the quiz and answers at random.
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 Spring '08
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