Теория вероятностей. Барышева В.К - 39 стр.

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H
3
H
4
P (H
1
) = P (A
1
A
1
) =
6
10
·
5
9
=
30
90
; P (A | H
1
) = 0.95 · 0.95 = 0.9025;
P (H
2
) = P (A
1
A
2
) =
6
10
·
4
9
=
24
90
; P (A|H
2
) = 0.95 · 0.8 = 0.760;
P (H
3
) = P (A
2
A
1
) =
4
10
·
6
9
=
24
90
; P (A|H
3
) = 0.8 · 0.95 = 0.760;
P (H
4
) = P (A
2
A
2
) =
4
10
·
3
9
=
12
90
; P (A|H
4
) = 0.8 · 0.8 = 0.64;
P (A) = P (H
1
)P (A|H
1
) + P (H
2
)P (A|H
2
) +
+ P (H
3
)P (A|H
3
) + P (H
4
)P (A|H
4
) =
=
30
90
· 0.9025 + 2 ·
24
90
· 0.760 +
12
90
· 0.64 =
=
1
90
(30 · 0.9025 + 48 · 0.760 + 12 · 0.64) = 0.7915;
P (H
4
|A) =
P (H
4
) · P (A|H
4
)
P (A)
=
1
90
· 12 · 0.64
0.7915
=
1
90
· 7.68
0.7915
= 0.1078.
N
P = 0.73.

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