Теория вероятностей. Барышева В.К - 30 стр.

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ТПУ | Томск

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P (A) = 1 − P (A
1
A
2
A
3
A
4
A
5
) =
= 1 − P (A
1
) · P (A
2
) · P (A
3
) · P (A
4
) · P (A
5
) =
= 1 − 0.9 · 0.8 · 0.7 · 0.8 · 0.9 =
= 1 − 0.9
2
· 0.8
2
· 0.7 = 1 − 0.36288 = 0.63712.
N
1 2
3 4
H A A
i
i
A = (A
1
+A
2
)(A
3
+A
4
) A
1
+A
2
, A
3
+A
4
A
1
A
2
, A
3
A
4
P (A) = P (A
1
+ A
2
)(A
3
+ A
4
) = P (A
1
+ A
2
)P (A
3
+ A
4
) =
= [P (A
1
) + P (A
2
) − P (A
1
A
2
) · [P (A
3
) + P (A
4
) − P (A
3
A
4
)].
P (A
i
) = 1 − P (
A
i
) = 1 − P
i
P (A
1
) = 0.9; P (A
2
) = 0.8; P (A
3
) =
0.7; P (A
4
) = 0.6; P (A) = [0.9 + 0.8 − 0.9 · 0.8] [0.7 + 0.6 − 0.7 · 0.8] = 0.8624
P (A) = (1 − P
1
P
2
)(1 − P
3
P
4
) = (1 − 0.1 · 0.9)(1 − 0.3 · 0.4) = 0.8624. N

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