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EC 41 UCLA Fall 2008 – Sample Problems #5; RE Section 4.5 and Ch 5 material
Midterm 2 will cover material from Chapter 2, sections 2.4, 2.5, & 2.6 and Chapters 4 and 5
These problems will NOT be collected or graded, but they will be useful for studying for exams.

The following table is for a sample of 500 patients at a particular health maintenance organization (HMO).
 Use it for questions 1 & 2
S
m
o
k
e
r
N
o
n

S
m
o
k
e
r
Total:
Have Heart Disease:
50
40
90
Do Not Have Heart Disease:
100
310
410
Total:
150
350
500
Event
Probability
1) a)
Form a partition of the four categories to the right.
Smoker and disease = P(S
∩
D) =
 select an individual at random from the population
Smoker and no disease = P(S
∩
D ) =
C
of patients.
Report the probability for each of the four
Nonsmoker and disease = P(S
∩
D) =
C
possibilities.
Nonsmoker and no disease = P(S
∩
D
)
=
C
C
b)
It is impossible for an individual to be in two or more categories, thus the events are:
disjoint
or independent
2) a)
Select an individual at random from the population of 500 patients.
What is the probability they are
i) a smoker;
ii) nonsmoker?
Note, these two “events” also form a “partition of the sample space.”
What is the sum of the two
probabilities?
b)
Select an individual at random from the population of 500 patients.
What is the probability they are
i) have heart disease; ii) do not have heart disease?
c)
What it the probability of heart disease for a randomly chosen:
i) Smoker,
ii) Nonsmoker
d)
What it the probability an individual is a smoker for a randomly chosen person:
i) With Disease;
ii) Without Disease
e)
Is the probability the a randomly chosen individual (from the population of 500) is both a smoker and has heart disease equal
to the probability of a smoker times probability of heart disease?
Is it true that:
P(S
∩
D) = P(S)P(D)?
f)
Verify Bayes’ rule:
)
(
)

(
)
(
)

(
)
(
)

(
)

(
C
C
D
P
D
S
P
D
P
D
S
P
D
P
D
S
P
S
D
P
⋅
+
⋅
⋅
=
3)
Consider two events, A and B.
P(A) =.10; P(BA) =.80; P(BA
C
) =.30
a) Probability of the complement of A: P(A
C
)
=
b) Probability of A given B: P(AB) =
c) Unconditional probability of B: P(B) =
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This note was uploaded on 03/07/2010 for the course ECON 41 taught by Professor Guggenberger during the Spring '07 term at UCLA.
 Spring '07
 Guggenberger

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