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Homework 1
•
Homework must be answered in the order shown here (else please make a note telling the
reader where it is).
•
Write your answers neatly
•
Work must be shown for full credit
•
No late homework accepted under any circumstances
1.
A die is rolled continually until a 6 appears, at which point the experiment stops. What is the
sample space of this experiment?
Let E
n
denote the event that n rolls are necessary to complete
the experiment. What points of the sample space are contained in E
n
? What is
?
2.
Two dice are thrown. Let E be the event that the sum of the dice is odd; let F be the event that
at least one of the dice lands on 1; and let G be the event that the sum is 5. Describe the events
EF,
E
∪
F
, FG,
EF
c
, and EFG.
3.
A, B, C take turns in flipping a coin. The first one to get a head wins. The sample space of
this experiment can be defined by
(a) Interpret the sample space
(b) Define the following events in terms of S:
(i) A wins = A
(ii) B wins=B
(iii) (A
∪
B)
c
4.
A system is composed of 5 components, each of which is either working or failed. Consider an
experiment that consists of observing the status of each component, and let the outcome of the
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 Summer '07
 Wu
 Probability

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