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EE 131A
Homework #3
Spring 2008
Due April 23rd
K. Yao
Read LeonGarcia (3rd edition), pp. 97–104; 141146.
1. A batch of 500 containers of frozen orange juice contains 5 that are defective. Two are
selected randomly one after the other without replacement.
a.
What is the probability that the second one selected is defective given that the ﬁrst
one was defective?
b.
What is the probability that both are defective?
c.
What is the probability that both are nondefective?
2. In the above problem, let A and B denote the events that the ﬁrst and second container
selected is defective, respectively.
a.
Are A and B independent events?
b
If the sampling were done with replacement, would A and B be independent?
3. Use the fact
P
(
D
∪
E
) =
P
(
D
)+
P
(
E
)

P
(
D
∩
E
) and standard rules of set operations
to prove
P
(
A
∪
B
∪
C
) =
P
(
A
) +
P
(
B
) +
P
(
C
)

P
(
A
∩
B
)

P
(
A
∩
C
)

P
(
B
∩
C
) +
P
(
A
∩
B
∩
C
)
.
4. A number
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This note was uploaded on 04/12/2010 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.
 Spring '08
 LORENZELLI

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