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Fall 20072008, Prof. Shachter
HOMEWORK #2 SOLUTIONS
CHAPTER #2
PROBLEMS
12)
a) Using Proposition 4.4, we have
P(student in Spanish class
U
student in French class
U
student in German class)
=1/100 x [(28+26+16) – (12+4+6) + 2] = 0.5
P(student not taking any of these classes)
= 1 – 0.5 = 0.5
b)
# students taking exactly Spanish = 28 – (12+4) + 2 = 14
# students taking exactly French = 26 – (12+6) + 2 = 10
# students taking exactly German = 16 – (4+6) + 2 = 8
P(students taking exactly one class)
= 1/100 x (14+10+8) =0.32
c)
P(at least one student is taking a language class)
= 1 –
P(neither student is taking a language class)
= 1 – (50/100 x 49/99)
= 0.7525
15)
a) First we pick 1 suit out of 4, and then 5 ranks out of the 13 ranks in the suit.
# ways to make a flush =
5
13
1
4
Hence
P(flush)
=
5
52
5
13
1
4
=
0.00198
b) We first determine the number of ways to make a onepair 5 card hand. This is
equivalent to choosing one of the 13 ranks (Ace to King) in a standard deck, choosing
two suits with these ranks, choosing 3 different ranks of the remaining 12, and of each of
those 3 ranks choosing one suit.
Thus # of ways to make a onepair hand =
1
4
1
4
1
4
3
12
2
4
1
13
= 1098240
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View Full DocumentThus
P(one pair)
=
5
52
1098240
= 0.4226
c) We have a similar situation here, except we choose two distinct ranks from 13, from
which we choose 2 out of 4 suits for the first rank and for the second, and finally, choose
one from the final 44 cards left over.
# of ways to make twopair hand =
1
4
1
11
2
4
2
4
2
13
= 123552
Thus
P(two pair)
=
5
52
123552
= 0.0475
d) By the same reasoning as above,
# ways to make 3 of a kind =
1
4
1
4
2
12
3
4
1
13
= 54912
Thus
P(3 of a kind)
=
5
52
54912
= 0.0211
e)
# ways to make 4 of a kind =
1
4
1
12
4
4
1
13
= 624
Thus
P(4 of a kind)
=
5
52
624
= 0.00024
21)
a)
P(#children = 1)
= 4/20 = 0.2
P(#children = 2)
= 8/20 = 0.4
P(#children = 3
) = 5/20 = 0.25
P(#children = 4
) = 2/20 = 0.1
P(#children = 5)
= 1/20 = 0.05
Total # of children = 4+16+15+8+5=48
P(child from family with 1 child)
= 4/48=0.08333
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This note was uploaded on 02/10/2010 for the course MS&E 120 taught by Professor Shatcher during the Spring '08 term at Stanford.
 Spring '08
 SHATCHER

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