o******r
发帖数: 1378 | | l***n
发帖数: 1270 | | w**********n
发帖数: 3624 | | s***s
发帖数: 4329 | | t***n
发帖数: 546 | 5 b不对吧。
随便选有50%机会选中B？
这题没有答案吧 | g********r
发帖数: 4248 | 6 kao,
if A!=B!=C!=D!, 25%.
however, TWO 25%
means 50%
if 50%, then should select 25%
then
cycle
【在 o******r 的大作中提到】
| s******d
发帖数: 424 | | o******1
发帖数: 12177 | 8 推难了，云里雾里
【在 o******r 的大作中提到】
| g**a
发帖数: 2129 | 9 i thought the probability would be 1/3. | b*****n
发帖数: 482 | 10 Suppose we randomly pick a, b, c, and d, then
if a/d is correct, the chance to be correct is 50%
if b is correct, the chance to be correct is 25%
if c is correct, the chance to be correct is 25%
Let P(a/d) to be the possibility of a/d is the correct answer
P(b) to be the possibility of b is the correct answer
P(c) to be the possibility of c is the correct answer
and P(total) to be the possibility of getting the correct answer
Then we have
P(total) = P(a/d) * 50% + P(b) * 25% + (1-P(a/d)-P(b)) * 25%
= P(a/d)*0.5 + P(b)*0.25 + 0.25 - P(a/d)*0.25 - P(b)*0.25
= P(a/d)*0.25 + 0.25
Since one of the answers is correct, P(total) would have value of 25%,
50%
or 60%.
if P(total) = 0.25, we get P(a/d) = 0, which means a, d is not the
correct
answer, which is a conflict.
if P(total) = 0.5, we get P(a/d) = 1, which means only a, d can be the
correct answer, which is also a conflict (since P(total)=0.5 means b is
the
correct answer)
if P(total) = 0.6, we get P(a/d) = 1.4, which is not possible.
Therefore this question has no answer.
However, if either b or c is in the range of (0.25, 0.5), then we can
possibly get a correct answer based on P(a/b).
For example, if choice b is 45%, c is something else (not 25% or 45%).
Then
for P(total) = 0.45, we get P(a/d) = 0.8. In that case, as long as a/d
has
80% chance to be the correct answer, the possibility that we pick the
correct answer will be exactly 45%. Since
P(total) = P(a/d)*0.5 + P(b)*0.25 + P(c)*.025
= P(a/d)*0.5 + (P(b)+P(c)) * 0.25
= 0.8 * 0.5 + 0.2 * 0.25
= 0.45
# | | | g**a
发帖数: 2129 | 11 Define event space S1 as the collections of choosing one option.
S1={A,B,C,D}
define event space S2 as the all possible correct answer
S2={a1,a2,a3}(any numbers are fine. Here based on the question a1=0.25, a2=0
.5, a3=0.6)
S1US2={Aa1,Aa2,Aa3,Ba1,Ba2,Ba3,Ca1,Ca2,Ca3,Da1,Da2,Da3}=the collection of
events that the status of your choice
Within all those 12 events, you are making correct choice in 3 events
Aa1,Ba2,Ca3,Da1
So the probability of making correct choice is 4/12=1/3 | l*****y
发帖数: 58 | 12 首先要假设有一个确定的0到1 之间的数 来使得"be correct"有意义。
0 is a consistant answer.
你只要给出正确答案， 没人说这是一道选择题。 http://i.imgur.com/qvzU4.jpg | a*******r
发帖数: 288 | | s***s
发帖数: 4329 | 14 有3个不同的答案，随机选的话答对的概率肯定小于50％
没一个对 | N***i
发帖数: 4104 | 15 假设“chance...correct”这个值是存在的话，首先不可能等于25%，因为这样一来选
中的概率就是50%，自相矛盾。
既然正确答案不是25%，那么随机选中的概率就不可能等于或者大于50%，于是剩下两个
答案也是错的。
【在 o******r 的大作中提到】
| s*********h
发帖数: 6288 | 16 Wrong. If there is a correct answer, the value of answer is not r.v. hence
can say "probability that b is correct answer."
actually, there is no correct answer, can be proved easily by contradiction.
【在 b*****n 的大作中提到】
: Suppose we randomly pick a, b, c, and d, then
: if a/d is correct, the chance to be correct is 50%
: if b is correct, the chance to be correct is 25%
: if c is correct, the chance to be correct is 25%
: Let P(a/d) to be the possibility of a/d is the correct answer
: P(b) to be the possibility of b is the correct answer
: P(c) to be the possibility of c is the correct answer
: and P(total) to be the possibility of getting the correct answer
: Then we have
: P(total) = P(a/d) * 50% + P(b) * 25% + (1-P(a/d)-P(b)) * 25%
| y*****r
发帖数: 1295 | 17 “我这句话是假话。”
我上面这句话是真还是假？
现有逻辑是不完备的。良好定义的命题不一定可以判定真伪。数学系统里，只要包含自
然数，也必定不完备。由哥德尔证明。
这样的著名数学命题有连续统问题（实数之间能否插进其它数），希尔伯特第十问题（
是否有判定丢番图方程存在整数解的算法），都是颇为高深的例子。
这么简单的数学悖论命题，我还是第一次看到，有点意思。（当然也许不是悖论，是我
自己没有功力得出正确答案。）
【在 o******r 的大作中提到】
| i******y
发帖数: 119 | 18 Don't be fooled by the question.
The answer is A or D. 25%.
【在 o******r 的大作中提到】
| i******y
发帖数: 119 | 19 Don't be fooled by the question.
It asks you for the chance of selecting one out of four options, not for how
many options give you the correct number.
【在 g********r 的大作中提到】
: kao,
: if A!=B!=C!=D!, 25%.
: however, TWO 25%
: means 50%
: if 50%, then should select 25%
: then
: cycle
| w**********n
发帖数: 3624 | | P******e
发帖数: 1598 | 21 当你回答B的时候，答案自动变成a/d了
【在 w**********n 的大作中提到】
: B
| o******r
发帖数: 1378 | 22 faint..這麼多回复。。 這個題沒有正確答案吧
【在 o******r 的大作中提到】
|
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