HW 1, due Thursday 09/03/2009, 10:00 AM
1. A box contains 3 marbles: one red, one green, and on blue. Consider an experiment
that consists of taking one marble from the box then replacing it in the box and drawing
a second marble from the box. What is the sample space? If, at all times, each marble
in the box is equally likely to be selected, what is the probability of each point in the
sample space?
2. Let
E
,
F
,
G
be three events. Find expressions for the events that of
E
,
F
,
G
,
a.
at least one event occurs
b.
both
E
and
F
but not
G
occurs.
c.
all three events occurs.
d.
at most one occurs.
e.
at most two occurs.
f.
none occurs.
3. The probability that Mary will fail a certain exam is 0
.
6, the probability that Bill will
fail the exam is 0
.
5, and the probability of both will fail is 0
.
3.
a.
What is the probability that at least one of them will fail?
b.
What is the probability that neither of them will fail?
c.
What is the probability that exactly one of them will fail?
4. If a fair coin is tossed 4 times, what is the probability that we get exactly 2 heads?
5. Redo the last problem if the coin is biased, that for each toss the chance of getting a
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 Fall '09
 Jin
 Probability, Probability theory, Dice

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