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ISyE 2027
Probability with Applications
Fall 2006
R. D. Foley
Homework 2
August 30, 2006
due on Tuesday, 5 September
1. (a) If we toss a coin once and then roll a die once, what would be a
reasonable sample space
S
? (b) How many outcomes are in your sample
space? (c) If we assume the die and coin are fair, are the outcomes equally
likely?
2. Suppose we have a sample space with Pr(
A
) =
.
4, Pr(
B
) =
.
3, and Pr(
A
∩
B
) =
.
1. Compute (a) Pr(
¯
A
), where
¯
A
denotes the complement of
A
, (b)
Pr(
A
∪
B
), (c) Pr(
¯
A
∩
¯
B
), and (d) Pr(
¯
A
∪
¯
B
). (e) Are
A
and
B
disjoint?
3. (a) If Georgia license plates are 3 numbers followed by 3 letters, how many
possible license plates are there? (b) How many of the license plates do
not have any repeated digits or letters?
4. Compute
(
6
2
)
,
(
6
1
)
and
(
6
0
)
.
5. How many diﬀerent four person committees can be made from 10 diﬀerent
people? How many diﬀerent sets of oﬃcers (president, vice president,
treasurer, and secretary) can be selected from 10 people?
6. Suppose we randomly grab 3 balls without replacement from an urn con
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