h**********o
发帖数: 37 | 1 70% students choose class A
80%students choose class B
85% students choose class C
90% students choose class D
what is the minimum probability for students choose all ABCD classes.
I think it is 70%+80%-1=50%.
Am I right? |
e***y
发帖数: 49 | 2 加起来，减3
【在 h**********o 的大作中提到】
: 70% students choose class A
: 80%students choose class B
: 85% students choose class C
: 90% students choose class D
: what is the minimum probability for students choose all ABCD classes.
: I think it is 70%+80%-1=50%.
: Am I right?
|
h**********o
发帖数: 37 | 3 不懂，理由是什么？
【在 e***y 的大作中提到】
: 加起来，减3
|
k*****n
发帖数: 117 | 4 Gees... your problem statement is not clear at all.
Let me try to restate the problem
There is a group of students and there are 4 classes - A, B, C and D.
For each class, each student may choose it or not choose it.
After they made up their decisions, we find
70% chose A, 80% chose B, 85% chose C, and 90% chose D.
Now what is the maximum and minimum possible percentage of students who
chose all four classes. |
r*********n
发帖数: 4553 | 5 P(AB)=P(A)+P(B)-1
P(ABC)=P(AB)+P(C)-1
P(ABCD)=P(ABC)+P(D)-1 = total sum -3
at each step the whole space is filled -> minimum overlap at each step ->
overall minimum overlap
【在 h**********o 的大作中提到】
: 不懂，理由是什么？
|
h**********o
发帖数: 37 | |
s****e
发帖数: 638 | 7
for A == B == C == D == 0.5
P(ABCD) = 2-3 = -1
【在 r*********n 的大作中提到】
: P(AB)=P(A)+P(B)-1
: P(ABC)=P(AB)+P(C)-1
: P(ABCD)=P(ABC)+P(D)-1 = total sum -3
: at each step the whole space is filled -> minimum overlap at each step ->
: overall minimum overlap
|
e***y
发帖数: 49 | 8 不要闹了，加起来小于3 ，min of p(ABCD)=0
【在 s****e 的大作中提到】
:
: for A == B == C == D == 0.5
: P(ABCD) = 2-3 = -1
|
r*********n
发帖数: 4553 | 9 if P(A)+P(B)<1, it simply means there would be no overlap, the answer is 0
of course the way i wrote it is not rigorous
【在 s****e 的大作中提到】
:
: for A == B == C == D == 0.5
: P(ABCD) = 2-3 = -1
|
s**********r
发帖数: 8153 | |
|
|
a**l
发帖数: 38 | 11 min 25% max 70%画个图就知道了。 |
r**s
发帖数: 17 | 12 正解
【在 a**l 的大作中提到】
: min 25% max 70%画个图就知道了。
|
l*****n
发帖数: 114 | 13 min: 1-((1-0.7)+(1-0.8)+(1-0.85)+(1-0.9))=0.25
max: 0.7
【在 h**********o 的大作中提到】
: 70% students choose class A
: 80%students choose class B
: 85% students choose class C
: 90% students choose class D
: what is the minimum probability for students choose all ABCD classes.
: I think it is 70%+80%-1=50%.
: Am I right?
|
t**c
发帖数: 539 | 14 P(AB)=P(A)+P(B)-P(A or B) >= P(A)+P(B) - 1
P(ABC) ＝ Ｐ(ＡＢ)＋Ｐ(Ｃ)－Ｐ(ＡＢｏｒＣ) >＝ Ｐ(ＡＢ)＋Ｐ(Ｃ)－１ >＝
Ｐ(Ａ)＋Ｐ(Ｂ)＋Ｐ(Ｃ)－２
ｓｉｍｉｌａｒｙ: Ｐ(ＡＢＣＤ) >＝ Ｐ(Ａ)＋Ｐ(Ｂ)＋Ｐ(Ｃ)＋Ｐ(Ｄ) －３
【在 r*********n 的大作中提到】
: P(AB)=P(A)+P(B)-1
: P(ABC)=P(AB)+P(C)-1
: P(ABCD)=P(ABC)+P(D)-1 = total sum -3
: at each step the whole space is filled -> minimum overlap at each step ->
: overall minimum overlap
|
e*********r
发帖数: 80 | |
