Chapter 3.
P1
10
·
1
36
(36

6)
·
1
36
= 1
/
3
P5
6
2
6 + 9
2
·
9
2
4 + 9
2
=
6
91
P7
For simplicity, do not consider twins. From the four equally likely possibilities
(he, sister), (he, brother), (sister, he), (brother, he) (where the elder child is listed
first) the last one should not be regarded because the elder brother becomes the
king. From the three remaining cases, in two he has a sister. So the answer is 2/3.
P8
1/2
P10
13

2
52

2
. This can be seen directly or from the formula of conditional proba
bility:
P
(the first is spade

the second and the third are spades) =
P
(
all three are spades
)
P
(
the second and the third are spades
)
=
13
3
/
52
3
13
2
/
52
2
=
11
50
P17 (a)
P
(
DC
) =
P
(
D
)
·
P
(
C

D
) =
.
36
·
.
22 =
.
0792
(b)
P
(
D

C
) =
P
(
DC
)
P
(
C
)
=
.
0792
.
3
=
.
264
P18 (d)
P
(
V
) =
P
(
V I
) +
P
(
V L
) +
P
(
V C
) =
P
(
I
)
·
P
(
V

I
) +
P
(
L
)
·
P
(
V

L
) +
P
(
C
)
·
P
(
V

C
) =
.
46
·
.
35 +
.
30
·
.
62 +
.
24
·
.
48 =
.
4862 (or 48.62%)
(a)
P
(
I

V
) =
P
(
IV
)
P
(
V
)
=
P
(
I
)
·
P
(
V

I
)
P
(
V
)
=
.
46
·
.
35
.
4862
=
.
331
...
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 Spring '08
 Moumen,F
 Trigraph, Sibling, 9 m, 48.62%, The Elder Brother

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