ORIE 3500/5500 Fall Term 2008
Assignment 1
Note that
•
the due date is
Monday September 15
at 1:00 pm
•
you need to mention your section number on the top of your answer
script.
1. [3 + 4 + 3 = 10 pts]
Suppose
A
and
B
are two events.
(a) If
P
(
A
) = 0
.
55,
P
(
B
c
) = 0
.
35 and
P
(
A
∪
B
) = 0
.
75, then deter
mine
P
(
A
∩
B
)
,P
(
A
c
∩
B
) and
P
(
A
∩
B
c
).
(b) Show that
(
A
∪
B
)
∩
(
A
∩
B
)
c
= (
A
c
∩
B
)
∪
(
A
∩
B
c
)
.
(c) Use part (b) to show that
P
((
A
c
∩
B
)
∪
(
A
∩
B
c
)) =
P
(
A
) +
P
(
B
)

2
P
(
A
∩
B
)
.
2. [2 + 2 + 2 = 6 pts]
We roll a foursided die and then we roll it as many times as is necessary
to obtain a diﬀerent face than the one obtained in the ﬁrst roll. Let
the outcome be (
r
1
,r
2
), where
r
1
and
r
2
are the results of the ﬁrst and
last rolls respectively. Assume that all possible outcomes are equally
likely. Find the probability that
(a)
r
1
is even.
(b) Both
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 Fall '08
 TODD
 Conditional Probability, Probability, Summation, Roll, foursided die

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