Practice Problems
1.
Suppose that
P(A) = 0.60
and
P(B) = 0.50.
a)
Can
A
and
B
be mutually exclusive?
Why or why not?
What is the minimum
possible value of
P(A
∩
B)?
What is the maximum possible value of
P(A
∩
B)?
b)
What is the minimum possible value of
P(A
∪
B)?
What is the maximum possible
value of
P(A
∪
B)?
2.
Suppose that
P(A) = 0.40
and
P(B) = 0.30.
a)
Can
A
and
B
be mutually exclusive?
Why or why not?
What is the minimum
possible value of
P(A
∩
B)?
What is the maximum possible value of
P(A
∩
B)?
b)
What is the minimum possible value of
P(A
∪
B)?
What is the maximum possible
value of
P(A
∪
B)?
3.
Consider two events,
A
and
B
,
such that
P(A) = 0.70
,
P(B) = 0.40
and
P(A
∪
B) = 0.82.
Are
A
and
B
independent?
4.
The CPA examination has four parts, one each on accounting problems, auditing,
business law, and the theory of accounting.
To be certified, an applicant must
pass all four parts.
Past history shows that on the first attempt 30% pass the
accounting part, 35% pass auditing, 30% pass law, and 20% pass theory.
a)
If success on one part of the examination is independent of success on any other
part, what is the probability that an applicant becomes certified on the first
attempt to pass the CPA examination?
b)
Do you believe that this probability is a reasonable approximation if you know
that more than 10% of applicants pass all four parts of the examination on their
first attempt?
Comment on the assumption of independence among parts of the
test.
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5.
500 people, all of whom drive approximately 10,000 miles per year, were
classified according to age and the number of auto accidents each has had
during the last three years:
Number of
Age (in years)
Accidents
Under 40
Over 40
0
170
80
1
80
70
More than 1
50
50
A person is selected at random from those 500.
a)
What is the probability that the person selected is over 40 and has had more than 1
accident?
b)
What is the probability that the person selected is either over 40 or has had more
than 1 accident (or both)?
c)
Find the probability that the person selected is over 40 given that he/she has had
more than 1 accident.
d)
Suppose that the person selected is over 40.
What is the probability that he/she has
had more than 1 accident?
e)
Find the probability that the person selected is over 40 given that he/she has had
at most 1 accident.
f)
Find the probability that the person selected has had more than 1 accident given
that he/she has had at least one accident.
6.
A building has three elevators.
The first elevator is waiting at the first floor 40%
of the time, the second one is waiting there 20% of the time, and the third elevator
is waiting at the first floor with probability 0.25.
Assume that all three elevators
operate independently.
a)
What is the probability that all three elevators are waiting on the first floor?
b)
What is the probability that at least one elevator is waiting on the first floor?
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 Spring '08
 Kim
 Statistics, Mutually Exclusive, Normal Distribution, Probability, Probability theory, probability density function, Cumulative distribution function

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