IE 111
NAME
_______Solutions___________
9:00 Section
Exam 1.2a
Fall 2011
Instructions
•
Open book, open notes
•
Clearly indicate your answer
•
You must show all relevant work and justify your answers appropriately
•
Partial credit will be given, but not without sufficient support
•
Factorials, permutations, combinations and other complex formulas do not need to be
evaluated.
You can leave as
4
C
2
for example.
•
Cases where you should compute a final number are noted.
•
Each question is worth 25 points
•
My guess is that this is a long test.
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Question 1
Consider the events shown in the Venn diagram above:
Suppose P(A)=0.3
P(B)=0.1
P(C)=0.5
P(D)=0.2
P(AB)=0.1.
Suppose also that A
and C are independent.
(Please compute a final probability for each part).
a)
Find P(C
′∩
D)
= 0 since (C
′∩
D)=
∅
b)
Find P(C
′∩
D
′
)
= P(C
′
) = 1P(C) = 0.5
c)
Find P(A
′∩
B
′∩
D)
= P(D) = 0.2
d)
Find P(A
∪
C
∪
D)
= P(A
∪
C) = P(A)+P(C) P(A
∩
C)
= 0.3+0.5(0.3)(0.5) = 0.65
e)
Find P(A
∪
B)
= P(A)+P(B) P(A
∩
B)
= P(A)+P(B) P(AB) P(B)
= 0.3 + 0.1 – (0.1)(0.1)
= 0.39
Question 2
Two players, player A and player B each roll a single, fair, six sided die (i.e. a regular
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 Fall '07
 Storer
 Probability

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