IE 111 Fall Semester 2007
Homework #2 Solutions
Note: these are not necessarily in order from easy to hard.
They should keep you busy,
some are pretty tricky, have fun.
Question 1.
Three fair coins are tossed.
Find the following:
a) P(TTT)
b) P(TTH)
c) P(more heads than tails)
d) P(more heads than tails  at least one tail)
e) P(Exactly one head  at least two tails
a)
1/8
b)
1/8
c)
4/8
d)
TTT,TTH,THT,HTT,THH,HTH,HHT: 3/7
e)
TTT,TTH,THT,HTT: ¾
Question 2.
There are 4 men and 5 women at a meeting.
a)
How many ways are there to select a committee of 3 people?
9
C
3
b)
How many ways are there to select a committee of 3 people if
exactly
one must be
male?
4
C
1
*
5
C
2
c)
How many ways are there to select a committee of 3 people if
at least
one must be
male?
4
C
1
*
5
C
2
+
4
C
2
*
5
C
1
+
4
C
3
*
5
C
0
or equivalently
9
C
3

5
C
3
Question 3.
There are 40 ping pong balls labeled from 1 to 40 in the picksix lotto game.
Six balls are
picked randomly (without replacement) from the 40.
What is the probability that the 6
numbers picked are the same as the six numbers you picked earlier in the day?
1/(
40
C
6
)
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View Full DocumentQuestion 4.
a) For a nine person baseball team, how many different batting orders are there?
9!
b) A bar sells 12 varieties of domestic beer and 8 varieties of imported beer.
How many
ways are there to select 3 (different) domestic and 4 (different) imported brands?
(
12
C
3
)(
8
C
4
)
c) An urn contains 5 blue, 6 red, and 7 black marbles.
You draw 4 marbles without
replacement.
Given
that you got no blue marbles, what is the probability that you got
exactly 2 red marbles?
(
6
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 Spring '07
 Storer
 Probability, World Series, TwoFace, Phillies, Mozart piano concertos

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