100
CHAPTER
2
Fundamentals of Discrete Probability
Dana Meseroll thought things over. She felt very uneasy about the possibility
of
installing
the GLAN, having it not perform
up to specifications,
and suffering
the
embarrassment
of having to rebuild it, reship it, and reinstall it. She guessed that this
embarrassment
could cost the company around $100,000 in lost goodwill, reputation,
and/or
effects on future earnings.
Assignment:
If you were Dana Meseroll, what decision strategy would you recommend?
EXERCISES
EXERCISE2.1A foursided die is engraved with the numbers 1 through 4 on its
four different sides. Suppose that when rolled, each side (and hence each number)
has an equal probability of being the bottom face when it lands. Weroll two such
dice. Let X be the sum of the numbers on the bottom faces of the two dice.
(a) What is the probability that X is at least five?
(b) How does your answer to (a) change if you are told that the bottom face of
the
first die
has the number "3" on it?
(c)
How does your answer to (a) change if you are told that the bottom face of
oneof
the dice
has the number
"3" on it?
EXERCISE 2.2 We toss a coin three times. Let the outcome
of this experiment
be the
sequence
of heads
(H) and tails (T) resulting
from the three tosses.
(a)
Enumerate
all of the possible outcomes of this experiment.
(b)
What is the probability
of the outcome "HHT"?
(c)
What is the probability
of the event "The first two tosses resulted in heads"?
(d)
What is the probability
of the event "There were two heads in a row among the
three tosses"?
EXEROSE 2.3Suppose that there are 100MBA students in the firstyear class. Of these
students, 20 of them have two years of work experience, 30 have three years of work
experience,
15 have four years of work experience, and 35 have five or more years of
work experience. Suppose that a firstyear MBA student is selected at random.
(a)
What is the probability that this student has at least four years of work experience?
(b)
Suppose that you are told that this student
has at least three years of work expe
rience. What is the conditional probability that this student has at least four years
of work experience?
EXERCISE 2.4 An oil company
is drilling
for oil at three promising
sites. Accord
ing to geological
tests, the probabilities
of finding
oil at these three sites are 0.70,
0.85, and 0.80, respectively.
The presence
of oil at anyone
of the sites is presumed
to be independent
of the presence
of oil at any of the other sites.
(a)
What is the probability
of finding oil at all three of the sites?
(b)
What is the probability
of not finding oil at any of the three sites?
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 Spring '07
 JosephGeunes
 Probability, Standard Deviation, Probability theory

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