Теория вероятностей. Барышева В.К - 36 стр.

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ТПУ | Томск

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P (A | H
1
) =
1800
4000
=
9
20
, P (A | H
2
) =
1500
6000
=
5
20
.
P (A) = P (H
1
)P (A | H
1
) + P (H
2
)P (A | H
2
) =
= 0, 4 ·
9
20
+ 0, 6 ·
5
20
=
1
20
(3, 6 + 3) =
6, 6
20
= 0.3.
P (H
1
|A) =
P (H
1
)P (A|H
1
)
P (A)
=
0.4 ·
9
20
6.6
20
=
=
0.4 · 9
6.6
=
3.6
6.6
=
6
11
= 0.55.
H A
H
1
H
2
H
3
P (H
1
) =
30
100
= 0.3; P (H
2
) =
20
100
= 0.2; P (H
3
) =
50
100
= 0.5.
P (A | H
1
) =
80
100
= 0.8; P (A | H
2
) =
90
100
= 0.9;
P (A | H
3
) =
95
100
= 0.95.
P (A) = P (H
1
) · P (A | H
1
) + P (H
2
) · P (A | H
2
) +
+ P (H
3
) · P (A | H
3
) =
= 0.3 · 0.8 + 0.2 · 0.9 + 0.5 · 0.95 = 0.895.

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