Ch1 1
x4 a0a2a1a2a3a2a4a2a5a2a6a2a7a2a8a2a9
a10a2a11a2a12a2a13a2a14a2a15a17a16
a18 4.1
a19
a13a2a20a2a21a2a22a2a23a17a24a26a25
A = a27a2a28a2a29a2a30 6 a31a2a32a2a33
a24
B = a34a2a28a2a29a2a30 3 a31a2a32a2a33
a16
a35a37a36 P(A)a24 P(B)a24a39a38a37a40a37a41a37a42a37a43a37a44a37a45a37a46a47a16a49a48a2a42a2a50a52a51a53a23a2a46a2a54a2a55a52a56a57a24
a27a2a28a2a29a2a30 6 a31
a32a37a33a37a58
a24a60a59a37a61a63a62a2a46a2a42a65a64a53a66
a34a63a28a2a67
a56a69a68a2a70
a31a63a32a2a33
a16a72a71a53a73a47a24a75a74a63a76a2a77a2a78a63a50 A
a79a37a80
a46
a81a2a82a2a78a17a24 B
a79a2a80
a46a2a83a2a84a17a24a26a85a2a68a63a86a2a87a63a88a2a89a47a16a90a38a63a91
a34a63a28a2a29a63a30a63a92a2a31a63a32a2a33
a46a63a83a2a84a63a42
C37C1032=C1339:
a93a2a94a2a25a2a95 P(BjA)a24a26a96a2a95 A
a79a2a80
a46a2a97a2a98a2a78a17a24 B a46a2a97a2a98a2a83a2a84a17a16
a18 4.2
a99a2a28a2a100
a68a2a12a63a13a63a101a103a102a104a24a106a105a103a77a63a13a63a101a103a102a63a42a103a107a63a102a103a108a63a109a103a102a63a46a63a83a103a84a63a110a111a64a112a24a106a113
a114a2a115
P a116a118a117a2a28
a68a2a77a2a107a2a77a2a109a111a119 = 1=2
P a116a118a117a2a28
a68a2a77a2a107a2a77a2a109 j
a120a2a121
a68a2a77a2a13a2a109a2a102a111a119 = 2=3
a50a2a122a2a123a2a83a2a124a52a56a125a24a26a68a2a78a63a126a2a46a63a127a63a128a2a61a63a129a2a130
a116a132a131 P(A) 6= 0a119a132a133
P(BjA) = P(AB)=P(A):
a131 A a79a37a80
a46a37a68a37a134a37a135a37a136a2a95 m(A)a24 A
a79a37a80 B a137a37a79a37a80
a46a37a68a37a134a37a135a37a136a2a95 m(AB)a24
a113 a114a2a115
P(BjA) = m(AB)=m(B) = P(AB)=P(A):
a97a2a98a2a83a2a84
a137
a42a2a83a2a84a17a24a26a94a63a138a63a139a104a133
(1)P( jA) = 1;
(2)P(BjA) > 0;
(3)Bi
a140a2a141
a110a2a142a17a24 i =1a24 2a24 a24 na24a26a113 P(Pn
i=1 Bi) = P(A);
a143a53a97a2a98a2a83a2a84a2a144a2a130a2a145a2a146 a114a2a147a63a148
a30
a78a63a126a2a46a63a149a2a150a63a144a63a130a104a133
P(AB) = P(B)P(AjB) = P(A)P(BjA):
a143a53a151a2a152a2a150 a114a2a147a2a148
a30
a78a2a126a2a46a63a85a2a77a63a153a63a46a2a149a63a150a2a144a63a130a104a133
P(A1A2 An) = P(A1)P(A2jA1)P(A3jA1A2) P(AnjA1A2 An 1):
1
Ch1 2
x5a154
a3a2a8a2a9a2a5a2a155a2a3a2a8a2a9
1,a154
a3a2a8a2a9
a156
a131 A1a24 A2a24 a24 An a42a158a157a158a128a158a159a161a160 a46a158a77a158a13a158a162a158a163a164a24a112a165 Ai a12a158a12
a141
a110
a166a17a24 P(A
i) > 0
a24a26a167 Pn
i=1 Ai =
a24a26a113a2a35a2a168a2a88a2a46 Ba24a26a68 B = Pn
i=1 BAi
a24
P(B) =
nX
i=1
P(BAi) =
nX
i=1
P(Ai)P(BjAi):
a18 5.1
a116a170a169a37a171a37a172a37a173a2a174
a124a111a119
a169a2a171a2a175a63a176a2a169a2a177
a24a75a77a2a178a63a179a2a180a2a68 x
a181a37a169
a128a17a24a60a182a37a183
a28
a68 a x
a181a2a169
a128a47a24a184a156
a131
a105a63a185
a169a63a171a63a186
a46a63a83a63a84a63a41a63a95 pa24a184a187a2a188a2a178a2a179
a169a2a177a63a189a63a30a63a190
a56a69a77
a188a2a191a2a192a2a95a2a193a17a24a26a194
a169a63a171
a59
a58
a191a2a192a63a46a63a83a2a84a47a16
a195 a25
Ai = fa169a2a171
a178a2a179a2a68 i
a181
a59
a58
a191a2a192 ga24
B = fa196
a77a2a185
a169a2a171a2a186 ga24
a113a52a143a53a197a2a83a2a144a2a130
P(Ai) = P(AijB)P(B) + P(AijBc)P(Bc)
= pP(Ai+1) + qP(Ai 1)
a190
a56a125a24 q = 1 pa24a26a25 p
i = P(Ai)
a24a26a113a2a68
pi = ppi+1 + qpi 1;
a198 a136 p
0 = 1
a24 p
a = 0
a114a2a147a2a199a2a148
px =
8>
>>>
<
>>>
>:
q
p
x q
p
a
1 qp a; p 6= 12;
1 xa; p = 12
a200 a x a91a47a24a90a201a2a76
a169
a185a2a42a2a144a2a202a63a46a47a24a203a165 p = 1=2a24 p
x = 1 x=a 1
a24
a169a2a171
a59
a58a2a137
a70a2a204a2a205a2a206a2a207a2a191a2a192a47a16
2
Ch1 3
2,a155a2a3a2a8a2a9
a134a2a208a2a197a2a83a2a144a2a130a17a24a26a209a2a210 a114a2a147a63a148
a30
a78a63a126a2a46a63a211a63a83a2a144a63a130a47a16
a131 A1a24 A2a24 a24 An a42a112a157a112a128a112a159a104a160 a46a112a77a112a13a112a162a112a163a158a24a212a113a37a35a2a168a37a77a37a213a37a98 Ba24 P(B) >
0a24a26a68
P(AijB) = P(Ai)P(BjAi)nX
j=1
P(Aj)P(BjAj); i = 1; 2; ; n:
a214a37a215a37a216a37a42a37a77a37a217a37a218a2a20a2a219a2a220a2a46a2a216a37a221a47a24a222a182a224a223a225a81a2a95a2a193a2a41a2a42a2a226a2a54a52a227a53a228a2a229a2a230a2a231a2a232a2a233a2a42
a234a2a235a2a236a2a237 a214a2a215a2a216a17a16a238a48a63a42a17a24a239a227a69a228a2a229a63a230a2a46a63a240a63a232a2a84a63a68a63a241a2a242a63a243a65a244a60a11a63a11a2a78a63a126a63a46a2a14a63a15a47a16
a18 5.2 a226a37a54a164a227a245a228a37a229a2a230a47a24a246a214a2a215a2a216a63a247a2a248a63a249a2a250a2a251a63a252a2a253a2a254a63a255a1a0a3a2a2a46a2a83a63a84a2a42 0.99a24
a182a5a4a112a248a112a249a112a214a112a215a112a216a37a247a37a46a37a20a37a251a37a252a37a253a37a254a37a255a6a0a7a2a37a46a37a83a37a84a37a42 0.01a16a9a8a112a254a112a20a11a10a13a12a5a14a112a46 0.001
a95a2a214a2a215a2a216a2a247a2a248a2a249a2a250a17a24a246a194a63a77a2a13a63a20a2a50a63a251a2a252a63a253a2a254a63a255a1a0a3a2a2a46a16a15a18a17a63a78a17a24a26a86a63a87a16a19a2a42a63a214a2a215a63a216
a248a2a249a2a250a2a46a2a83a2a84a17a16
a195 a25
A = fa214a2a215a2a216a2a247a2a248a2a249a2a250 ga24
T = fa251a2a252a2a253a2a254a2a255a1a0a20a2 ga24
a68 P(A) = 0:001a24 P(TjA) = 0:99a24 P(TjAc) = 0:01a16a225a143a53a211a2a83a2a144a2a130
P(AjT) = P(TjA)P(A)P(TjA)P(A) + P(TjAc)P(Ac) = 0:09:
a137
a201a2a42a18a21a17a24a246a50a18a22a2a251a2a253a2a254a2a95a1a0a3a2a2a46a63a20 a200 a56a57a24a24a23a2a68
a141
a30a16a25
a162a16a26a2a77a63a46a2a20a63a42a18a27a16a28
a46a2a214a2a215a2a216a2a247a2a248a2a249a2a250a17a16a246a182a16a27a18a28a16a29a2a233a63a229a2a230a63a240a2a232a63a84a2a46a47a24a26a42a63a20a18a30a65a56a53a248a63a249a2a214a63a215a2a216a63a247a2a20a16a14
a31a1a32 a46a1a33a53a14a17a24a24a34a18a4a63a248a63a249a2a214a63a215a2a216a63a247a63a46a2a20a16a22a2a251a63a253a63a254a2a95a35a0a3a2a2a46a63a83a2a84a47a16
x6 a36a18a37a18a38
a39a18a40 a96a2a12a2a13a2a213a2a98 Aa24 B a42a2a110
a140a18a41a18a42
a46a17a24a24a8a2a254
P(AB) = P(A)P(B):
a96a112a95
a41a5a42
a24 a42a164a71a245a95a18a8a37a254 Aa24 B a110
a140a5a41a5a42
a24 a201a37a68 P(BjA) = P(AB)=P(A) =
P(B)a24a26a201a2a42a18a21a17a24 A a46 a79a2a80a18a43
a141a18a44a18a45
B a79a2a80
a46 a114a18a46 a2a2a46a18a47a2a101a17a16
3
Ch1 4
a166a49a48a37a11a51a50a125a24 a24 ;
a52
a168a49a53a37a213a37a98a2a41
a41a18a42
a16a54a8a63a254 A
a52 B
a41a49a42
a24 A
a52 Bca24 Ac a52
Ba24 Ac a52 Bc a41a2a42
a41a18a42
a46a17a16
a39a18a40 a96 Aa24 Ba24 C a42a2a110
a140a18a41a18a42
a46a17a24a24a8a63a254a2a68
8>
>>>
<
>>>
>:
P(AB) = P(A)P(B);
P(BC) = P(B)P(C);
P(CA) = P(C)P(A);
P(ABC) = P(A)P(B)P(C):
a55a18a56a2a46a17a24 a114a2a147 a233a2a89 n a13a2a213a2a98 A
1
a24 A
2
a24 a24 A
n
a46
a41a18a42
a2a47a133
a39a18a40 a96 A
1
a24 A
2
a24 a24 A
n
a42a2a110
a140a18a41a18a42
a46a17a24a24a8a2a254a63a35a63a36a2a168a63a88a63a46a58a57 a206a16a14 k(2 6
k 6 n) a147a18a59 a138a2a139 1 6 i1 6 i2 6 6 in 6 n a46 k a13a58a57a225a206a18a14 i1a24 i2a24 a24 in a41
a68
P(A1A2 An) = P(A1)P(A2) P(An):
a18 6.2
a99
a124a18a60a2a46a2a242a18a61a18a62a52a56a53a84a2a95 0.6a16a64a63a2a50a2a208a18a65a18a66a1a67a20a61a52a64a53a91
a79a16a68 a116
a105a16a61
a68
a77
a79
a119a118a24a70a69a53a207 a147 0.99 a147 a19a2a46a18a71a18a72a18a73a52a56a53a77a18a74a18a75a18a76a47a24
a120a63a121a16a77a16a78
a70a35a67a69a242a18a61a111a244
a195
a131a18a79
a207 n a67a53a242a18a61a17a24
a43
a25
Ai = a196 i a67a53a242a18a61a18a73a52a56a20a75a18a76a17a24 i = 1; 2; ; n;
B = a75a18a76a18a80a18a73a52a56a125a16
a81 a88
a30
B = A1 [ A2 [ [ An;
Bc = Ac1 \ Ac2 \ \ Acn;
a82 n
a83
a138a2a139
P(Bc) = P(Ac1Ac2 Acn) 6 0:01:
a143a53a36 A
1
a24 A
2
a24 a24 A
n
a42a2a110
a140a18a41a18a42
a46a17a24a24a82 Ac
1
a24 Ac
2
a24 a24 Ac
n a137
a42a2a110
a140a18a41a18a42
a46a17a16
a31 a147
P(Bc) = P(Ac1Ac2 Acn) = (1 0:6)n = 0:4n 6 0:01;
a114a2a115 n > 5:027a24a26a165
a120a2a121a18a79
a207 6 a67a53a242a18a61a17a16
a38a18a84a2a207a18a85a18a86a18a87a1a50a125a24a246a12a2a12
a41a18a42
a43
a141
a46a18a88 a50a53a110
a140a18a41a16a42
a16a26a201
a92
a13a2a213a63a98a2a110
a140a18a41a16a42
a231a18a21a17a24 P(ABC) = P(A)P(B)P(C) a42
a141
a114a18a89
a121
a46a17a24a26a78a63a126a2a201a63a42a63a77a2a13a63a14a2a15a47a16
4
Ch1 5
a18 6.1 a93a2a77a2a13a18a28a2a188a2a146a63a162a103a95
a19a3a90
a24a91a63a16a92a16a76a94a93
a190
a56a69a77
a90
a24 Aa24 Ba24 C a162a18a86a18a95
a96 a31 a93 a148 a77
a90a18a97
a50a18a98a18a99a16a100a63a162a17a24a101a19a16a99a18a100a63a162a47a24a102a98a16a19a16a34a18a103a63a78a47a24a102a104a63a78a1a105a57a16
A B C
a105 1.4
a48 a115
P(A) = P(B) = P(C) = 1=2;
P(AB) = P(BC) = P(CA) = 1=4;
a48a2a42
P(ABC) = 1=4 6= P(A)P(B)P(C) = 1=8;
a38a18a21a1a106 Aa24 Ba24 C a42a2a12a2a12
a41a18a42
a46a17a24a26a48
a141
a42a63a110
a140a18a41a16a42
a46a47a16
5
x4 a0a2a1a2a3a2a4a2a5a2a6a2a7a2a8a2a9
a10a2a11a2a12a2a13a2a14a2a15a17a16
a18 4.1
a19
a13a2a20a2a21a2a22a2a23a17a24a26a25
A = a27a2a28a2a29a2a30 6 a31a2a32a2a33
a24
B = a34a2a28a2a29a2a30 3 a31a2a32a2a33
a16
a35a37a36 P(A)a24 P(B)a24a39a38a37a40a37a41a37a42a37a43a37a44a37a45a37a46a47a16a49a48a2a42a2a50a52a51a53a23a2a46a2a54a2a55a52a56a57a24
a27a2a28a2a29a2a30 6 a31
a32a37a33a37a58
a24a60a59a37a61a63a62a2a46a2a42a65a64a53a66
a34a63a28a2a67
a56a69a68a2a70
a31a63a32a2a33
a16a72a71a53a73a47a24a75a74a63a76a2a77a2a78a63a50 A
a79a37a80
a46
a81a2a82a2a78a17a24 B
a79a2a80
a46a2a83a2a84a17a24a26a85a2a68a63a86a2a87a63a88a2a89a47a16a90a38a63a91
a34a63a28a2a29a63a30a63a92a2a31a63a32a2a33
a46a63a83a2a84a63a42
C37C1032=C1339:
a93a2a94a2a25a2a95 P(BjA)a24a26a96a2a95 A
a79a2a80
a46a2a97a2a98a2a78a17a24 B a46a2a97a2a98a2a83a2a84a17a16
a18 4.2
a99a2a28a2a100
a68a2a12a63a13a63a101a103a102a104a24a106a105a103a77a63a13a63a101a103a102a63a42a103a107a63a102a103a108a63a109a103a102a63a46a63a83a103a84a63a110a111a64a112a24a106a113
a114a2a115
P a116a118a117a2a28
a68a2a77a2a107a2a77a2a109a111a119 = 1=2
P a116a118a117a2a28
a68a2a77a2a107a2a77a2a109 j
a120a2a121
a68a2a77a2a13a2a109a2a102a111a119 = 2=3
a50a2a122a2a123a2a83a2a124a52a56a125a24a26a68a2a78a63a126a2a46a63a127a63a128a2a61a63a129a2a130
a116a132a131 P(A) 6= 0a119a132a133
P(BjA) = P(AB)=P(A):
a131 A a79a37a80
a46a37a68a37a134a37a135a37a136a2a95 m(A)a24 A
a79a37a80 B a137a37a79a37a80
a46a37a68a37a134a37a135a37a136a2a95 m(AB)a24
a113 a114a2a115
P(BjA) = m(AB)=m(B) = P(AB)=P(A):
a97a2a98a2a83a2a84
a137
a42a2a83a2a84a17a24a26a94a63a138a63a139a104a133
(1)P( jA) = 1;
(2)P(BjA) > 0;
(3)Bi
a140a2a141
a110a2a142a17a24 i =1a24 2a24 a24 na24a26a113 P(Pn
i=1 Bi) = P(A);
a143a53a97a2a98a2a83a2a84a2a144a2a130a2a145a2a146 a114a2a147a63a148
a30
a78a63a126a2a46a63a149a2a150a63a144a63a130a104a133
P(AB) = P(B)P(AjB) = P(A)P(BjA):
a143a53a151a2a152a2a150 a114a2a147a2a148
a30
a78a2a126a2a46a63a85a2a77a63a153a63a46a2a149a63a150a2a144a63a130a104a133
P(A1A2 An) = P(A1)P(A2jA1)P(A3jA1A2) P(AnjA1A2 An 1):
1
Ch1 2
x5a154
a3a2a8a2a9a2a5a2a155a2a3a2a8a2a9
1,a154
a3a2a8a2a9
a156
a131 A1a24 A2a24 a24 An a42a158a157a158a128a158a159a161a160 a46a158a77a158a13a158a162a158a163a164a24a112a165 Ai a12a158a12
a141
a110
a166a17a24 P(A
i) > 0
a24a26a167 Pn
i=1 Ai =
a24a26a113a2a35a2a168a2a88a2a46 Ba24a26a68 B = Pn
i=1 BAi
a24
P(B) =
nX
i=1
P(BAi) =
nX
i=1
P(Ai)P(BjAi):
a18 5.1
a116a170a169a37a171a37a172a37a173a2a174
a124a111a119
a169a2a171a2a175a63a176a2a169a2a177
a24a75a77a2a178a63a179a2a180a2a68 x
a181a37a169
a128a17a24a60a182a37a183
a28
a68 a x
a181a2a169
a128a47a24a184a156
a131
a105a63a185
a169a63a171a63a186
a46a63a83a63a84a63a41a63a95 pa24a184a187a2a188a2a178a2a179
a169a2a177a63a189a63a30a63a190
a56a69a77
a188a2a191a2a192a2a95a2a193a17a24a26a194
a169a63a171
a59
a58
a191a2a192a63a46a63a83a2a84a47a16
a195 a25
Ai = fa169a2a171
a178a2a179a2a68 i
a181
a59
a58
a191a2a192 ga24
B = fa196
a77a2a185
a169a2a171a2a186 ga24
a113a52a143a53a197a2a83a2a144a2a130
P(Ai) = P(AijB)P(B) + P(AijBc)P(Bc)
= pP(Ai+1) + qP(Ai 1)
a190
a56a125a24 q = 1 pa24a26a25 p
i = P(Ai)
a24a26a113a2a68
pi = ppi+1 + qpi 1;
a198 a136 p
0 = 1
a24 p
a = 0
a114a2a147a2a199a2a148
px =
8>
>>>
<
>>>
>:
q
p
x q
p
a
1 qp a; p 6= 12;
1 xa; p = 12
a200 a x a91a47a24a90a201a2a76
a169
a185a2a42a2a144a2a202a63a46a47a24a203a165 p = 1=2a24 p
x = 1 x=a 1
a24
a169a2a171
a59
a58a2a137
a70a2a204a2a205a2a206a2a207a2a191a2a192a47a16
2
Ch1 3
2,a155a2a3a2a8a2a9
a134a2a208a2a197a2a83a2a144a2a130a17a24a26a209a2a210 a114a2a147a63a148
a30
a78a63a126a2a46a63a211a63a83a2a144a63a130a47a16
a131 A1a24 A2a24 a24 An a42a112a157a112a128a112a159a104a160 a46a112a77a112a13a112a162a112a163a158a24a212a113a37a35a2a168a37a77a37a213a37a98 Ba24 P(B) >
0a24a26a68
P(AijB) = P(Ai)P(BjAi)nX
j=1
P(Aj)P(BjAj); i = 1; 2; ; n:
a214a37a215a37a216a37a42a37a77a37a217a37a218a2a20a2a219a2a220a2a46a2a216a37a221a47a24a222a182a224a223a225a81a2a95a2a193a2a41a2a42a2a226a2a54a52a227a53a228a2a229a2a230a2a231a2a232a2a233a2a42
a234a2a235a2a236a2a237 a214a2a215a2a216a17a16a238a48a63a42a17a24a239a227a69a228a2a229a63a230a2a46a63a240a63a232a2a84a63a68a63a241a2a242a63a243a65a244a60a11a63a11a2a78a63a126a63a46a2a14a63a15a47a16
a18 5.2 a226a37a54a164a227a245a228a37a229a2a230a47a24a246a214a2a215a2a216a63a247a2a248a63a249a2a250a2a251a63a252a2a253a2a254a63a255a1a0a3a2a2a46a2a83a63a84a2a42 0.99a24
a182a5a4a112a248a112a249a112a214a112a215a112a216a37a247a37a46a37a20a37a251a37a252a37a253a37a254a37a255a6a0a7a2a37a46a37a83a37a84a37a42 0.01a16a9a8a112a254a112a20a11a10a13a12a5a14a112a46 0.001
a95a2a214a2a215a2a216a2a247a2a248a2a249a2a250a17a24a246a194a63a77a2a13a63a20a2a50a63a251a2a252a63a253a2a254a63a255a1a0a3a2a2a46a16a15a18a17a63a78a17a24a26a86a63a87a16a19a2a42a63a214a2a215a63a216
a248a2a249a2a250a2a46a2a83a2a84a17a16
a195 a25
A = fa214a2a215a2a216a2a247a2a248a2a249a2a250 ga24
T = fa251a2a252a2a253a2a254a2a255a1a0a20a2 ga24
a68 P(A) = 0:001a24 P(TjA) = 0:99a24 P(TjAc) = 0:01a16a225a143a53a211a2a83a2a144a2a130
P(AjT) = P(TjA)P(A)P(TjA)P(A) + P(TjAc)P(Ac) = 0:09:
a137
a201a2a42a18a21a17a24a246a50a18a22a2a251a2a253a2a254a2a95a1a0a3a2a2a46a63a20 a200 a56a57a24a24a23a2a68
a141
a30a16a25
a162a16a26a2a77a63a46a2a20a63a42a18a27a16a28
a46a2a214a2a215a2a216a2a247a2a248a2a249a2a250a17a16a246a182a16a27a18a28a16a29a2a233a63a229a2a230a63a240a2a232a63a84a2a46a47a24a26a42a63a20a18a30a65a56a53a248a63a249a2a214a63a215a2a216a63a247a2a20a16a14
a31a1a32 a46a1a33a53a14a17a24a24a34a18a4a63a248a63a249a2a214a63a215a2a216a63a247a63a46a2a20a16a22a2a251a63a253a63a254a2a95a35a0a3a2a2a46a63a83a2a84a47a16
x6 a36a18a37a18a38
a39a18a40 a96a2a12a2a13a2a213a2a98 Aa24 B a42a2a110
a140a18a41a18a42
a46a17a24a24a8a2a254
P(AB) = P(A)P(B):
a96a112a95
a41a5a42
a24 a42a164a71a245a95a18a8a37a254 Aa24 B a110
a140a5a41a5a42
a24 a201a37a68 P(BjA) = P(AB)=P(A) =
P(B)a24a26a201a2a42a18a21a17a24 A a46 a79a2a80a18a43
a141a18a44a18a45
B a79a2a80
a46 a114a18a46 a2a2a46a18a47a2a101a17a16
3
Ch1 4
a166a49a48a37a11a51a50a125a24 a24 ;
a52
a168a49a53a37a213a37a98a2a41
a41a18a42
a16a54a8a63a254 A
a52 B
a41a49a42
a24 A
a52 Bca24 Ac a52
Ba24 Ac a52 Bc a41a2a42
a41a18a42
a46a17a16
a39a18a40 a96 Aa24 Ba24 C a42a2a110
a140a18a41a18a42
a46a17a24a24a8a63a254a2a68
8>
>>>
<
>>>
>:
P(AB) = P(A)P(B);
P(BC) = P(B)P(C);
P(CA) = P(C)P(A);
P(ABC) = P(A)P(B)P(C):
a55a18a56a2a46a17a24 a114a2a147 a233a2a89 n a13a2a213a2a98 A
1
a24 A
2
a24 a24 A
n
a46
a41a18a42
a2a47a133
a39a18a40 a96 A
1
a24 A
2
a24 a24 A
n
a42a2a110
a140a18a41a18a42
a46a17a24a24a8a2a254a63a35a63a36a2a168a63a88a63a46a58a57 a206a16a14 k(2 6
k 6 n) a147a18a59 a138a2a139 1 6 i1 6 i2 6 6 in 6 n a46 k a13a58a57a225a206a18a14 i1a24 i2a24 a24 in a41
a68
P(A1A2 An) = P(A1)P(A2) P(An):
a18 6.2
a99
a124a18a60a2a46a2a242a18a61a18a62a52a56a53a84a2a95 0.6a16a64a63a2a50a2a208a18a65a18a66a1a67a20a61a52a64a53a91
a79a16a68 a116
a105a16a61
a68
a77
a79
a119a118a24a70a69a53a207 a147 0.99 a147 a19a2a46a18a71a18a72a18a73a52a56a53a77a18a74a18a75a18a76a47a24
a120a63a121a16a77a16a78
a70a35a67a69a242a18a61a111a244
a195
a131a18a79
a207 n a67a53a242a18a61a17a24
a43
a25
Ai = a196 i a67a53a242a18a61a18a73a52a56a20a75a18a76a17a24 i = 1; 2; ; n;
B = a75a18a76a18a80a18a73a52a56a125a16
a81 a88
a30
B = A1 [ A2 [ [ An;
Bc = Ac1 \ Ac2 \ \ Acn;
a82 n
a83
a138a2a139
P(Bc) = P(Ac1Ac2 Acn) 6 0:01:
a143a53a36 A
1
a24 A
2
a24 a24 A
n
a42a2a110
a140a18a41a18a42
a46a17a24a24a82 Ac
1
a24 Ac
2
a24 a24 Ac
n a137
a42a2a110
a140a18a41a18a42
a46a17a16
a31 a147
P(Bc) = P(Ac1Ac2 Acn) = (1 0:6)n = 0:4n 6 0:01;
a114a2a115 n > 5:027a24a26a165
a120a2a121a18a79
a207 6 a67a53a242a18a61a17a16
a38a18a84a2a207a18a85a18a86a18a87a1a50a125a24a246a12a2a12
a41a18a42
a43
a141
a46a18a88 a50a53a110
a140a18a41a16a42
a16a26a201
a92
a13a2a213a63a98a2a110
a140a18a41a16a42
a231a18a21a17a24 P(ABC) = P(A)P(B)P(C) a42
a141
a114a18a89
a121
a46a17a24a26a78a63a126a2a201a63a42a63a77a2a13a63a14a2a15a47a16
4
Ch1 5
a18 6.1 a93a2a77a2a13a18a28a2a188a2a146a63a162a103a95
a19a3a90
a24a91a63a16a92a16a76a94a93
a190
a56a69a77
a90
a24 Aa24 Ba24 C a162a18a86a18a95
a96 a31 a93 a148 a77
a90a18a97
a50a18a98a18a99a16a100a63a162a17a24a101a19a16a99a18a100a63a162a47a24a102a98a16a19a16a34a18a103a63a78a47a24a102a104a63a78a1a105a57a16
A B C
a105 1.4
a48 a115
P(A) = P(B) = P(C) = 1=2;
P(AB) = P(BC) = P(CA) = 1=4;
a48a2a42
P(ABC) = 1=4 6= P(A)P(B)P(C) = 1=8;
a38a18a21a1a106 Aa24 Ba24 C a42a2a12a2a12
a41a18a42
a46a17a24a26a48
a141
a42a63a110
a140a18a41a16a42
a46a47a16
5
