m****r
发帖数: 141 | 1 【 以下文字转载自 Quant 讨论区 】
发信人: mitcar (mitcar), 信区: Quant
标 题: An interview question about probability.
发信站: BBS 未名空间站 (Sat Mar 17 21:13:44 2012, 美东)
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! |
p*****2
发帖数: 21240 | 2 第二题不是太明白。是说自己得seat和有prize得seat在剩下得10个里，还是怎的？ |
C***U
发帖数: 2406 | 3 P(B|A^c) = 1 - P(B^c|A^c) = 1 - 990/1000
这个不对
你已经知道你的座位空了，你就只能考虑999个座位了，而不是1000个。
the
your
【在 m****r 的大作中提到】
: 【 以下文字转载自 Quant 讨论区 】
: 发信人: mitcar (mitcar), 信区: Quant
: 标 题: An interview question about probability.
: 发信站: BBS 未名空间站 (Sat Mar 17 21:13:44 2012, 美东)
: 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
|
c**m
发帖数: 535 | 4 好像有问题。
如果这990个不是randomly移走的，而是保证移走没有price。
那么概率仍为1/1000。
这个题目跟那个三个门抽奖的很类似。 |
z*********8
发帖数: 2070 | |
H*****1
发帖数: 4815 | 6 q2
有10个seat left，其中有一个有奖
没有任何理由认为这其中任何一个比其他更有可能带奖或者更不可能带奖
所以你的概率是1/10
【在 m****r 的大作中提到】
: 【 以下文字转载自 Quant 讨论区 】
: 发信人: mitcar (mitcar), 信区: Quant
: 标 题: An interview question about probability.
: 发信站: BBS 未名空间站 (Sat Mar 17 21:13:44 2012, 美东)
: 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
|
p*****2
发帖数: 21240 | 7
我也是这样理解的。不过这也太简单了。怀疑题目没说清除。
【在 H*****1 的大作中提到】
: q2
: 有10个seat left，其中有一个有奖
: 没有任何理由认为这其中任何一个比其他更有可能带奖或者更不可能带奖
: 所以你的概率是1/10
|
z*********8
发帖数: 2070 | 8 你们可以自己手动测试一下， 把1000个座位换成3个座位， 看换和不换的概率区别
【在 p*****2 的大作中提到】
:
: 我也是这样理解的。不过这也太简单了。怀疑题目没说清除。
|
C***U
发帖数: 2406 | 9 但是理论上 你需要用bayes公式来算的
【在 H*****1 的大作中提到】
: q2
: 有10个seat left，其中有一个有奖
: 没有任何理由认为这其中任何一个比其他更有可能带奖或者更不可能带奖
: 所以你的概率是1/10
|
z****4
发帖数: 194 | 10 显然有理由啊。。。用bayes一算就知道还是1/1000
【在 H*****1 的大作中提到】
: q2
: 有10个seat left，其中有一个有奖
: 没有任何理由认为这其中任何一个比其他更有可能带奖或者更不可能带奖
: 所以你的概率是1/10
|
g*********e
发帖数: 14401 | 11 depends on whether the 990 seats were intentionally removed or just by luck.
If they were intentionally removed, p(current seat has gift)=1/1000 doesn't
change, you should switch to any of the remaining seats.
If the people who remove the seats doesn't know which seat has the gift, the
p remain the same. |
h********e
发帖数: 1972 | 12 就是车和门啊。。 都是1/1000. 所以如果只剩10个。。一定要换。这样中奖率就boost
了很多 |
