文科高等数学习题概率公式.
合集下载
相关主题
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
0.3 · 0.4
12
=
=
=.
P (B)P (A|B) + P (B)P (A|B) 0.3 · 0.4 + 0.7 · 0.1 19
14.
b(k; 10,
1 4
)
=
C1k0(
1 4
)k
(
3 4
)10−k
.
15. 100
1 − 0.99100.
C1100 · 0.01 · 0.9999;
1
P156, 5.3 P (A ∪ B) = P (A) + P (B) − P (A ∪ B)
1. P (A ∪ B) = P (AB) = 1 − P (AB) = 0.9. A = AB + AB, P (AB) = P (A) − P (AB) = 0.5. A ∪ B = BA = B − A, P (A ∪ B) = 1 − P (B − A) = 1 − (P (B) − P (AB)) = 0.8
(2)P (AB + AB) = P (AB) + P (AB)) = P (A)P (B) + P (A)P (B) = 0.1 ·
0.8 + 0.9 · 0.2 = 0.26.
9,10,11
A
9.
A
Ai
i
P (A) = P (A1 ∪ A2 ∪ A3) = 1 − P (A1A2A3) = 1 − P (A1)P (A2)P (A3) =
1
−
0.96
·
0.97
·
0.98
=
1366 15625
=
0.087424.
10. A1, A2, A3
P (A1 ∪ A2 ∪ A3) =
1
−
P (A1A2A3)
=
1
−
2 3
·
4 5
·
3 4
=
3 5
.
11.
1
−
(
1 2
)n
≥
99%
n, n = 7.
12. A1, A2, A3
B
.
2
P (A1) = 0.5, P (A2) = 0.2, P (A3) = 0.3, P (B|A1) = 0.6, P (B|A2) = 0.3, P (B|A3) = 0.8.
P (AB) = P (A)P (B).
7. A, B P (A) + P (B) − P (AB)
8. A, B
P (AB) = P (A)P (B),
P (A ∪ B) =
P (B)
=
P (A∪B)−P (A) 1−P (A)
=
0.4.
P (A) = 0.9, P (B) = 0.8
A, B
, (1) P (AB) = P (A)P (B) = 0.72.
2.
P (A ∪ B ∪ C) = P (A) + P (B) + P (C) − P (AB) − P (AC) −
P (BC)
+
P (ABC)
=
23 24
.
3. P (A ∪ B) = P (A) + P (B) − P (AB) = 0.2 + 0.3 − 0.1 = 0.4.
4. Ai
i
5. A, B
P (B) = P (A1)P (B|A1)+P (A2)P (B|A2)+P (A3)P (B|A3) = 0.5 · 0.6 + 0.2 · 0.3 + 0.3 · 0.8 = 0.6.
13, A
B
B, B
P (AB)
P (AB)
P (B|A) =
=
P (A) P (AB) + P (AB)
P (B)P (A|B)
2 3
.
6.
A, B
P (A|B)
=
P (AB) P (B)
.
P (A1A2)
=
P (A1)P (A2|A1)
=
95 100
·
5 99
=
95 1980
.
1500, 2000Biblioteka Baidu
P (B|A)
=
P (AB) P (A)
=
P (B) P (A)
=
P (A) = 1 − P (A) = 0.96,
P (B|A) = 0.75, P (B) = P (AB) = P (A)P (B|A) = 0.72.