Теория вероятностей. Барышева В.К - 31 стр.

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H A
i
i A
i
i
P (A
1
) = 0.9; P (A
2
) = 0.8; P (A
3
) = 0.7;
P (A
1
) = 0.1; P (A
2
) = 0.2; P (A
3
) = 0.3.
Ω =
A
1
A
2
A
3
; A
1
A
2
A
3
; A
1
A
2
A
3
; A
1
A
2
A
3
;
A
1
A
2
A
3
; A
1
A
2
A
3
; A
1
A
2
A
3
; A
1
A
2
A
3
.
A A = A
1
A
2
A
3
+ A
1
A
2
A
3
A
1
A
2
A
3
+ A
1
A
2
A
3
.
P (A) = P (A
1
A
2
A
3
+
A
1
A2A3 + A1A2A
3
+ A
1
A
2
A
3
) =
= P (A
1
A
2
A
3
) + P (A
1
A
2
A
3
) + P (A
1
A
2
A
3
) + P (A
1
A
2
A
3
) =
= P (A
1
)P (A
2
)P (A
3
) + P (A
1
)P (A
2
)P (A
3
)+
+ P (A
1
)P (A
2
)P (A
3
) + P (A
1
)P (A
2
)P (A
3
).
P (A) · · · ·
· · · ·
B
B = A
1
A
2
A
3
+ A
1
A
2
A
3
+ A
1
A
2
A
3
.
P (B) = P (A
1
A
2
A
3
+ A
1
A
2
A
3
+ A
1
A
2
A
3
) =
= P (A
1
A
2
A
3
) + P (A
1
A
2
A
3
) + P (A
1
A
2
A
3
) =
= 0.1 · 0.8 · 0.7 + 0.9 · 0.2 · 0.7 + 0.9 · 0.8 · 0.3 =
= 0.398.
C
C = A
1
A
2
A
3
+ A
1
A
2
A
3
+ A
1
A
2
A
3
+ A
1
A
2
A
3
.
P (C) = P (A
1
A
2
A
3
) + P (A
1
A
2
A
3
) + P (A
1
A
2
A
3
)+
+ P (A
1
A
2
A
3
) = 0.398 + 0.504 = 0.902.

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