2010 SPM 高级数学问题疑问。

hahabin

In selection of class monitor, probability of student x selected is 1/3, when the probability either student x or student y select is 2/5.
Find the probability that
A) Student Y is selected
这个应该属于Mutually exclusive event, 所以 2/5-1/3=1/15

B)Student Y or Student X is not selected
这个我有点疑惑，如果说Student Y or Student X is not selected 那么不是应该和Student X or student Y selected 的Probability一样？
又另外一个看法是说Student X or Student Y其中一个可以被选中另外一个也可以被选中或则两个都不中对吗？ 这样Probability 不是变成是 “1”？

多普勒效应

应用: P(A and B) = P(A) + P(B) - P(A or B).

hahabin

之前有想过用这个但是我找不到理由,可以麻烦你给我解释下你的看法吗？

hahabin

多普勒效应 发表于 1-7-2013 12:24 AM
应用: P(A and B) = P(A) + P(B) - P(A or B).

还是想不通，因为他说的是 A or B 怎么apply A and B?

BatuItu

问题是要选一名班长呢？还是多名班长？

BatuItu

如果问题是选一名班长

A) P(Y) = 2/5-1/3=1/15

B) 1- P(X or Y) = 3/5

BatuItu

如果问题是选多名班长

let interpret "either X or Y is selected" = "X or Y is selected but not both are selected"

A) P(Y) = P("either X or Y is selected" - P(X) + 2P(X and Y) = 2/5 - 1/3 + 2(0) = 1/15; assumed P(X and Y) =0

B)
P("either X or Y is not selected" =


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let assumed there are 4 students(X,Y,Z,A), and choose 2 monitors; the total elements set = {XY,XZ,XA,YZ,YA,ZA}

P(X) = p{XY,XZ,XA} = 1/3
P(Y) = P{XY,YZ,YA} = 1/15
P(X and Y) = P{XY} =0
P(X or Y) = P{XY,XZ,XA,YZ,YA} = P(X) + P(Y) - P(X and Y) =2/5
P("either X or Y is selected" = P{XZ,XA,YZ,YA} = P(X) + P(Y) - 2P(X and Y) =2/5
P("either X or Y is NOT selected" = P{XZ,XA,YZ,YA} = P("either X or Y is selected"

这个我有点疑惑，如果说Student Y or Student X is not selected 那么不是应该和Student X or student Y selected 的Probability一样？

P(''X and Y are not selected" = p{XZ,XA,YZ,YA,ZA} = 1 - P(X and Y) = 1

又另外一个看法是说Student X or Student Y其中一个可以被选中另外一个也可以被选中或则两个都不中对吗？ 这样Probability 不是变成是 “1”？

P("neither X nor Y is selected" = ???

PS：不过是我的看法，不管对错，加我5分

hahabin

BatuItu 发表于 2-7-2013 05:23 AM
如果问题是选一名班长

A) P(Y) = 2/5-1/3=1/15

应该只选一个，不过题目没有给我们了解释多名还是一名。所以我就假设一个来看。

可否解释为何 如果一名的话 B会是 1 - P(x or Y)?

BatuItu

hahabin 发表于 2-7-2013 10:05 AM
应该只选一个，不过题目没有给我们了解释多名还是一名。所以我就假设一个来看。

可否解释为何 如果一名 ...

只选一个的话

hmm。。我的看法：

let set = {x,y,甲,乙,丙,丁}

P(x or y) = P("x,y") = p(x) + p(y)

P(x or y)'= P("甲,乙,丙,丁") = 1 - P(x or y)

。。。

BatuItu

关于“either”

"Either A or B" most precisely means, in symbolic logic terms, "A XOR B", where XOR is the "exclusive or". So yes, it means "A or B but not both". It isn't always actually used with full precision, though, so, as usual, context has to be taken into account. If somebody says, "select either A or B", for example, they definitely mean that you should not select both. If they say "if either A or B is true", though, they probably mean a non-exclusive OR, and the condition is still true if both A and B are true. Unfortunately, if there's a generally reliable rule for telling which is meant, I'm failing to think of what it would be.

Without the "either", the presumption would be more toward "A OR B", where OR allows the case where both are true. Which is why computer geeks and propositional calculus nerds will, when asked "do you want to go to lunch now or later?", answer "yes". (Illustrating that the "either" part is implied by context as often as it's cancelled by context.)

http://english.stackexchange.com ... eclude-both-a-and-b