题目
题型:东城区一模难度:来源:
1 |
2 |
1 |
3 |
(Ⅰ)求至少有1人面试合格的概率;
(Ⅱ)求签约人数ξ的分布列和数学期望.
答案
由题意知A,B,C相互独立,
且P(A)=
1 |
2 |
1 |
3 |
至少有1人面试合格的概率是:
1-P(
. |
A |
. |
B |
. |
C |
=1-P(
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A |
. |
B |
. |
C |
=1-
1 |
2 |
2 |
3 |
2 |
3 |
=
7 |
9 |
(Ⅱ)ξ的可能取值为0,1,3.
P(ξ=0)=P(
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A |
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C |
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A |
. |
B |
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A |
. |
B |
. |
C |
=P(
. |
A |
. |
C |
. |
A |
. |
B |
. |
A |
. |
B |
. |
C |
=
1 |
2 |
1 |
3 |
2 |
3 |
1 |
2 |
2 |
3 |
1 |
3 |
1 |
2 |
2 |
3 |
2 |
3 |
=
4 |
9 |
P(ξ=1)=P(A
. |
B |
. |
C |
. |
B |
. |
C |
=P(A)P(
. |
B |
. |
C |
. |
B |
. |
C |
=
1 |
2 |
2 |
3 |
1 |
3 |
1 |
2 |
1 |
3 |
2 |
3 |
1 |
2 |
2 |
3 |
2 |
3 |
4 |
9 |
P(ξ=3)=P(ABC)=P(A)P(B)P(C)=
1 |
2 |
1 |
3 |
1 |
3 |
1 |
18 |
∴ξ的分布列是