Variation of the secretary problem
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N secretaries arrive at a job interview randomly ,
in each interview the secretary is either hired or rejected ,and you cant change that decision.
the interviewer uses the following strategy for choosing:
for some number a<1, the interviewer chooses the first secretary after the aN secretary,
that is better than all previous secretaries,
find a for which the probability of choosing the best or second best secretary is maximal.
assume N is a large enough number, write down the probability of success.
Im at a lost here,
probability probability-theory
asked Nov 20 at 21:06
user3184910
274
add a comment |
up vote
-1
down vote
favorite
N secretaries arrive at a job interview randomly ,
in each interview the secretary is either hired or rejected ,and you cant change that decision.
the interviewer uses the following strategy for choosing:
for some number a<1, the interviewer chooses the first secretary after the aN secretary,
that is better than all previous secretaries,
find a for which the probability of choosing the best or second best secretary is maximal.
assume N is a large enough number, write down the probability of success.
Im at a lost here,
probability probability-theory
asked Nov 20 at 21:06
user3184910
274
1
Are you familiar with the well-known very similar problem in which the selection algorithm is the same but object is to maximize the probability of finding the best secretay only? (The algorithm in that case is to choose the first secy after the first $N/e$ have been seen, who is better than all previous secretaries.)
– Mark Fischler
Nov 20 at 21:17
Im not familiar, but will read up on it now, thank you!
– user3184910
Nov 20 at 21:20
1
I think G.C. Rota did early paper on this but I could be wrong; he introduced me to the problem in the form of "Follow the tallest gang member" and his way of solving it was as I remember much more clever than anything I can think of today...
– Mark Fischler
Nov 20 at 21:54
While it makes sense to ask what factor $a$ gives the maximum probability (of choosing either the best or second best secretary), there are better approaches than the simple "one threshold" rule you've outlined.
– hardmath
Nov 27 at 6:15
This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.
– Did
16 hours ago
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
N secretaries arrive at a job interview randomly ,
in each interview the secretary is either hired or rejected ,and you cant change that decision.
the interviewer uses the following strategy for choosing:
for some number a<1, the interviewer chooses the first secretary after the aN secretary,
that is better than all previous secretaries,
find a for which the probability of choosing the best or second best secretary is maximal.
assume N is a large enough number, write down the probability of success.
Im at a lost here,
probability probability-theory
asked Nov 20 at 21:06
user3184910
274
N secretaries arrive at a job interview randomly ,
in each interview the secretary is either hired or rejected ,and you cant change that decision.
the interviewer uses the following strategy for choosing:
for some number a<1, the interviewer chooses the first secretary after the aN secretary,
that is better than all previous secretaries,
find a for which the probability of choosing the best or second best secretary is maximal.
assume N is a large enough number, write down the probability of success.
Im at a lost here,
probability probability-theory
probability probability-theory
asked Nov 20 at 21:06
user3184910
274
asked Nov 20 at 21:06
user3184910
274
asked Nov 20 at 21:06
user3184910
274
asked Nov 20 at 21:06
user3184910
274
asked Nov 20 at 21:06
user3184910
274
274
1
Are you familiar with the well-known very similar problem in which the selection algorithm is the same but object is to maximize the probability of finding the best secretay only? (The algorithm in that case is to choose the first secy after the first $N/e$ have been seen, who is better than all previous secretaries.)
– Mark Fischler
Nov 20 at 21:17
Im not familiar, but will read up on it now, thank you!
– user3184910
Nov 20 at 21:20
1
I think G.C. Rota did early paper on this but I could be wrong; he introduced me to the problem in the form of "Follow the tallest gang member" and his way of solving it was as I remember much more clever than anything I can think of today...
– Mark Fischler
Nov 20 at 21:54
While it makes sense to ask what factor $a$ gives the maximum probability (of choosing either the best or second best secretary), there are better approaches than the simple "one threshold" rule you've outlined.
– hardmath
Nov 27 at 6:15
This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.
– Did
16 hours ago
add a comment |
1
Are you familiar with the well-known very similar problem in which the selection algorithm is the same but object is to maximize the probability of finding the best secretay only? (The algorithm in that case is to choose the first secy after the first $N/e$ have been seen, who is better than all previous secretaries.)
– Mark Fischler
Nov 20 at 21:17
Im not familiar, but will read up on it now, thank you!
– user3184910
Nov 20 at 21:20
1
I think G.C. Rota did early paper on this but I could be wrong; he introduced me to the problem in the form of "Follow the tallest gang member" and his way of solving it was as I remember much more clever than anything I can think of today...
– Mark Fischler
Nov 20 at 21:54
While it makes sense to ask what factor $a$ gives the maximum probability (of choosing either the best or second best secretary), there are better approaches than the simple "one threshold" rule you've outlined.
– hardmath
Nov 27 at 6:15
This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.
– Did
16 hours ago
1
1
Are you familiar with the well-known very similar problem in which the selection algorithm is the same but object is to maximize the probability of finding the best secretay only? (The algorithm in that case is to choose the first secy after the first $N/e$ have been seen, who is better than all previous secretaries.)
– Mark Fischler
Nov 20 at 21:17
Are you familiar with the well-known very similar problem in which the selection algorithm is the same but object is to maximize the probability of finding the best secretay only? (The algorithm in that case is to choose the first secy after the first $N/e$ have been seen, who is better than all previous secretaries.)
– Mark Fischler
Nov 20 at 21:17
Im not familiar, but will read up on it now, thank you!
– user3184910
Nov 20 at 21:20
Im not familiar, but will read up on it now, thank you!
– user3184910
Nov 20 at 21:20
1
1
I think G.C. Rota did early paper on this but I could be wrong; he introduced me to the problem in the form of "Follow the tallest gang member" and his way of solving it was as I remember much more clever than anything I can think of today...
– Mark Fischler
Nov 20 at 21:54
I think G.C. Rota did early paper on this but I could be wrong; he introduced me to the problem in the form of "Follow the tallest gang member" and his way of solving it was as I remember much more clever than anything I can think of today...
– Mark Fischler
Nov 20 at 21:54
While it makes sense to ask what factor $a$ gives the maximum probability (of choosing either the best or second best secretary), there are better approaches than the simple "one threshold" rule you've outlined.
– hardmath
Nov 27 at 6:15
While it makes sense to ask what factor $a$ gives the maximum probability (of choosing either the best or second best secretary), there are better approaches than the simple "one threshold" rule you've outlined.
– hardmath
Nov 27 at 6:15
This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.
– Did
16 hours ago
This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.
– Did
16 hours ago
add a comment |
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1
Are you familiar with the well-known very similar problem in which the selection algorithm is the same but object is to maximize the probability of finding the best secretay only? (The algorithm in that case is to choose the first secy after the first $N/e$ have been seen, who is better than all previous secretaries.)
– Mark Fischler
Nov 20 at 21:17
Im not familiar, but will read up on it now, thank you!
– user3184910
Nov 20 at 21:20
1
I think G.C. Rota did early paper on this but I could be wrong; he introduced me to the problem in the form of "Follow the tallest gang member" and his way of solving it was as I remember much more clever than anything I can think of today...
– Mark Fischler
Nov 20 at 21:54
While it makes sense to ask what factor $a$ gives the maximum probability (of choosing either the best or second best secretary), there are better approaches than the simple "one threshold" rule you've outlined.
– hardmath
Nov 27 at 6:15
This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc.
– Did
16 hours ago