Теория вероятностей. Барышева В.К - 38 стр.

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H A B
H
1
H
2
P (H
1
) : P (H
2
) = 5 : 3. P (H
1
)+P (H
2
) = 1.
P (H
1
) = 5/8, P (H
2
) = 3/8.
P (A|H
1
) =
3
5
, P(A|H
2
) =
1
3
,
P (B|H
1
) =
2
5
, P(B|H
2
) =
2
3
.
A B
P (A) =
5
8
·
3
5
+
3
8
·
1
3
=
1
2
, P(B) =
5
8
·
2
5
+
3
8
·
2
3
=
1
2
.
P (H
1
|A) =
P (H
1
)P (A|H
1
)
P (A)
=
5
8
·
3
5
1/2
=
3
4
;
P (H
2
|B) =
P (H
2
)P (B|H
2
)
P (B)
=
3
8
·
2
3
1/2
=
1
2
.
N
H
A
1
A
2
Ω = {A
1
A
1
, A
1
A
2
, A
2
A
1
, A
2
A
2
}
H
1
H
2