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【 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!
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!
