m****r
发帖数: 141 | 1 An interview question about probability.
You enter a stadium with 1000 seats. you are told that under one of the
chairs is a prize. You choose a seat randomly.
q1, what's the probability your seat has a prize
q2, now 990 seats are removed, not including your seat or the one with the
prize under it. There are 10 seats left. What's the probability that your
seat contains the prize now?
My answer to q1: 1/1000
Q2:
A: my seat has a price , B: 990 empty
P(A|B) = P(B|A)P(A) / ( P(B|A)P(A) + P(B|A^c)P(A^c) )
P(B|A)P(A) = 1/1000
P(B|A^c)P(A^c) = (1 - 990/1000) * 999/1000 = 0.01
P(B|A^c) = 1 - P(B^c|A^c) = 1 - 990/1000
Here, A^c is A's complement.
So, it is = 1/1000 / ( 1 /1000 + 0.01)=0.0909
right ?
Any help is really appreciated.
Thanks a lot! |
j***y
发帖数: 1069 | 2 990把空椅子是从除你之外的999把里面选的 而且没选到prize
所以我觉得
P(Bc|Ac) = (998/999)*(997/998)*....(9/10) = 1/111
P(B) = 1/111*999/1000 + 1/1000 = 0.01
然后 P(A|B) = 0.1
小学生的话做这个题的话肯定直接猜到最后一步了 |
s*********y
发帖数: 45 | 3 为什么我觉得两题的答案都是 1／1000 呢？ 别人搬椅子跟你有啥子关系啊。。。。 |
e**********n
发帖数: 359 | 4 别人搬椅子的时候不能搬有奖品的椅子和有人坐的椅子。如果你坐到了奖品，别人有C^
990_999种拿法，如果你没坐到，别人有C^990_998种拿法。
【在 s*********y 的大作中提到】
: 为什么我觉得两题的答案都是 1／1000 呢？ 别人搬椅子跟你有啥子关系啊。。。。
|
d******o
发帖数: 59 | |
g******e
发帖数: 140 | 6 .001
【在 m****r 的大作中提到】
: An interview question about probability.
: You enter a stadium with 1000 seats. you are told that under one of the
: chairs is a prize. You choose a seat randomly.
: q1, what's the probability your seat has a prize
: q2, now 990 seats are removed, not including your seat or the one with the
: prize under it. There are 10 seats left. What's the probability that your
: seat contains the prize now?
: My answer to q1: 1/1000
: Q2:
: A: my seat has a price , B: 990 empty
|
m****r
发帖数: 141 | 7 jsyyy, please explain your solution, thanks
why
P(B) = P(Bc|Ac)P(Ac) + P(B|A)P(A) = 1/111*999/1000 + 1/1000 = 0.01 ?
thanks
【在 j***y 的大作中提到】
: 990把空椅子是从除你之外的999把里面选的 而且没选到prize
: 所以我觉得
: P(Bc|Ac) = (998/999)*(997/998)*....(9/10) = 1/111
: P(B) = 1/111*999/1000 + 1/1000 = 0.01
: 然后 P(A|B) = 0.1
: 小学生的话做这个题的话肯定直接猜到最后一步了
|
d******1
发帖数: 1389 | 8 这个跟那个绿皮书上，开门是羊还是车的题是一样的吧。
【在 m****r 的大作中提到】
: An interview question about probability.
: You enter a stadium with 1000 seats. you are told that under one of the
: chairs is a prize. You choose a seat randomly.
: q1, what's the probability your seat has a prize
: q2, now 990 seats are removed, not including your seat or the one with the
: prize under it. There are 10 seats left. What's the probability that your
: seat contains the prize now?
: My answer to q1: 1/1000
: Q2:
: A: my seat has a price , B: 990 empty
|
m****r
发帖数: 141 | 9 they are similar, but the difference is :
In green book , there is 2/3 probability to choose a door w/o price.
So, switching is better than not.
Here, we still have 9 possible choices to make in the remaining 10 seats.
【在 d******1 的大作中提到】
: 这个跟那个绿皮书上，开门是羊还是车的题是一样的吧。
|
k*****y
发帖数: 744 | 10 The second question is different from Monty Hall problem, since you do not
make another choice later, right?
Removing the chairs does not tell you any useful information about your
choice before. It does not exclude any sample event. So the answer remains 1
/1000.
【在 m****r 的大作中提到】
: An interview question about probability.
: You enter a stadium with 1000 seats. you are told that under one of the
: chairs is a prize. You choose a seat randomly.
: q1, what's the probability your seat has a prize
: q2, now 990 seats are removed, not including your seat or the one with the
: prize under it. There are 10 seats left. What's the probability that your
: seat contains the prize now?
: My answer to q1: 1/1000
: Q2:
: A: my seat has a price , B: 990 empty
|
|
|
c*******g
发帖数: 71 | 11 my 2c.
This question is no different from the Monty Hall problem. Prob remains to
be 1/1000 in Q2 since removing 990 seats is independent of the prob of
correctly picking the prize seat in the beginning.
another way to think of it is:
1. the prob of being the prize seat is equivalent to the prob of winning if
you don't switch after removing 990 seats, which equals to prob(lose if
switching after 990).
2. prob(lose if switching after 990) is irrelevant to # seats removed, since
it equals to prob(A) where A is "the seat you picked is the prize seat at
the beginning".
3. Thus, prob(prize seat after 990 removed) = prob(win if do NOT switch
after 990) = prob(lose if switch after 990) = prob(A) = 1/1000
【在 m****r 的大作中提到】
: An interview question about probability.
: You enter a stadium with 1000 seats. you are told that under one of the
: chairs is a prize. You choose a seat randomly.
: q1, what's the probability your seat has a prize
: q2, now 990 seats are removed, not including your seat or the one with the
: prize under it. There are 10 seats left. What's the probability that your
: seat contains the prize now?
: My answer to q1: 1/1000
: Q2:
: A: my seat has a price , B: 990 empty
|
W******r
发帖数: 789 | 12 这道题有ambiguity，取决于你对“990 seats are removed, not including your seat or the one with the prize under it”这句话怎么理解。如果remove seats的人不知道prize在哪里，他只是随机remove 990 seats而刚好没有包括有prize那张，那么就应该用bayes公式来计算。如果他知道prize在哪里，有意识地避开，在剩下的seats里面remove 990 seats，那么答案就是1/1000. |
s*****c
发帖数: 753 | 13 The question is about 他知道prize在哪里，有意识地避开，在剩下的seats里面
remove 990 seats，那么答案就是1/1000.
And for LZ, if you can answer the way like WtMaster shows, give them two
scenarios, they you can have a very good impression on the interviewer.
seat or the one with the prize under it”这句话怎么理解。如果remove seats的
人不知道prize在哪里，他只是随机remove 990 seats而刚好没有包括有prize那张，那
么就应该用bayes公式来计算。如果他知道prize在哪里，有意识地避开，在剩下的
seats里面remove 990 seats，那么答案就是1/1000.
【在 W******r 的大作中提到】
: 这道题有ambiguity，取决于你对“990 seats are removed, not including your seat or the one with the prize under it”这句话怎么理解。如果remove seats的人不知道prize在哪里，他只是随机remove 990 seats而刚好没有包括有prize那张，那么就应该用bayes公式来计算。如果他知道prize在哪里，有意识地避开，在剩下的seats里面remove 990 seats，那么答案就是1/1000.
|
m****r
发帖数: 141 | 14 I agree with WtMaster .
My understanding is:
如果remove seats的人不知道prize在哪里，他只是随机remove 990 seats而刚好没有
包括有prize那张
So, we have
P(B^c|A^c) = P(B^c & A^c)/ P(A^c) = (990/1000) / (999/1000) = 0.991
So, P(B|A^c) = 1 - P(B^c|A^c) = 1 - 0.991 = 0.009
So, P(B|A^c)P(A^c) = 0.009 * (999/1000) = 0.009
P(A|B) = P(B|A)P(A) / ( P(B|A)P(A) + P(B|A^c)P(A^c) &
#160; ) = 0.001/ (0.001+0.009) = 0.1
The result is 1/10.
Another point is that
Do we need to consider the problem of removing seats randomly with or
without including the seat I em sitting ?
If yes, the 1000 should be 999 event though the result may be still the same
.
thanks
seat or the one with the prize under it”这句话怎么理解。如果remove seats的
人不知道prize在哪里，他只是随机remove 990 seats而刚好没有包括有prize那张，那
么就应该用bayes公式来计算。如果他知道prize在哪里，有意识地避开，在剩下的
seats里面remove 990 seats，那么答案就是1/1000.
【在 W******r 的大作中提到】
: 这道题有ambiguity，取决于你对“990 seats are removed, not including your seat or the one with the prize under it”这句话怎么理解。如果remove seats的人不知道prize在哪里，他只是随机remove 990 seats而刚好没有包括有prize那张，那么就应该用bayes公式来计算。如果他知道prize在哪里，有意识地避开，在剩下的seats里面remove 990 seats，那么答案就是1/1000.
|
W******r
发帖数: 789 | 15 呵呵，你多虑了。你已经在坐着的椅子是绝对不会被搬走的。没有人会这样设计问题的。
without including the seat I em sitting ?
【在 m****r 的大作中提到】
: I agree with WtMaster .
: My understanding is:
: 如果remove seats的人不知道prize在哪里，他只是随机remove 990 seats而刚好没有
: 包括有prize那张
: So, we have
: P(B^c|A^c) = P(B^c & A^c)/ P(A^c) = (990/1000) / (999/1000) = 0.991
: So, P(B|A^c) = 1 - P(B^c|A^c) = 1 - 0.991 = 0.009
: So, P(B|A^c)P(A^c) = 0.009 * (999/1000) = 0.009
: P(A|B) = P(B|A)P(A) / ( P(B|A)P(A) + P(B|A^c)P(A^c) &
: #160; ) = 0.001/ (0.001+0.009) = 0.1
|
m****r
发帖数: 141 | 16 Just because I am sitting on a seat, the sample space size for removers is
999 not 1000, right ?
thanks
的。
【在 W******r 的大作中提到】
: 呵呵，你多虑了。你已经在坐着的椅子是绝对不会被搬走的。没有人会这样设计问题的。
:
: without including the seat I em sitting ?
|
W******r
发帖数: 789 | 17 Yes.
如果你想搏出位，我还有一个答案。不过不到万不得已不要使用，因为风险极大，面试
官不一定听得明白。
在你坐下来之后，你的座位有没有prize就已经是一个确定的事件了，根本就没有随机
性。随机性只存在于你的头脑里面，因为你不了解信息。对于他们知道内情的人来说这
是一个确定的事件。也就是说，不同的人因为所掌握的信息不同而建立了不同的概率模
型。对于你的概率模型，答案就是我们以上所讨论的。在他们的概率模型里，答案不是
0就是1。
【在 m****r 的大作中提到】
: Just because I am sitting on a seat, the sample space size for removers is
: 999 not 1000, right ?
: thanks
:
: 的。
|
