Econ 506, Section M
NAME:_
SOLUTION_
_____
Quiz 1B, Sept., 16, 2010
Total points: 50
I. (10 points)
A and B play tennis and P (A wins) = 0.3. Suppose that A and B play two
matches. What is the probability that A wins at least one match?
Let AB denotes the event that player A wins the first match and player B wins the
second. The sample space is S = {AA, AB, BA, BB}. Now the P ( A wins at least one
match) = P({AA, AB, BA}) = P({AA}) + P({AB}) + P({BA}) = 0.09 + 0.21 + 0.21 =
0.51
II.
(5 points)
If A and B are mutually exclusive events and P (B) > 0, show that
)
(
)
(
)
(
)

(
B
P
A
P
A
P
B
A
A
P
+
=
∪
.
III.
A delegation of three is to be chosen from the untenured faculty of the UIUC
Economics Department (numbering 8) to represent the department in an Institutewide
committee.
a)
(5 points)
in how many ways can the delegation be chosen?
56
3
8
=
=
r
n
b) (5 points)
in how many ways can the delegation be chosen if two people refuse to go
together?
We compute 56 #(Both are chosen to go together). There is only one way to choose
both of them in a combination sense. This leaves us with 6 different ways to pick the
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 Fall '08
 Staff
 Economics, Standard Deviation, mutually exclusive events

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