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09 Jun 2004, 12:26
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Guys, try to solve this interesting probability question
Assume that a beauty contest is being judged by the following rules: (1) there are N contestants not seen by the judges before the contest, and (2) the contestants are individually presented to the judges in a random sequence. Only one contestant appears before the judges at any one time. (3) The judges must decide on the spot whether the contestant appearing before them is the most beautiful. If they decide in the affirmative the contest is over but the risk is that a still more beautiful is in the group as yet not displayed. In that case the judges have made the wrong decision. On the other hand, if they pass over the candidate, the contestant is disqualified from further consideration even if it turns out that all subsequent candidates are less beautiful. What is the probability of correctly choosing the most beautiful contestant?
Assume that a beauty contest is being judged by the following rules: (1) there are N contestants not seen by the judges before the contest, and (2) the contestants are individually presented to the judges in a random sequence. Only one contestant appears before the judges at any one time. (3) The judges must decide on the spot whether the contestant appearing before them is the most beautiful. If they decide in the affirmative the contest is over but the risk is that a still more beautiful is in the group as yet not displayed. In that case the judges have made the wrong decision. On the other hand, if they pass over the candidate, the contestant is disqualified from further consideration even if it turns out that all subsequent candidates are less beautiful. What is the probability of correctly choosing the most beautiful contestant?
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09 Jun 2004, 13:30
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Let me try this again.
Assume 3 candidates are there A,B,C and A is the most beautiful
A can be shown to the judges in 3 ways. But total number of ways in which we can arrange A,B,C is 3! = 6 ways
P = 3/6 or n/n! = 1/(n-1)!
Assume 3 candidates are there A,B,C and A is the most beautiful
A can be shown to the judges in 3 ways. But total number of ways in which we can arrange A,B,C is 3! = 6 ways
P = 3/6 or n/n! = 1/(n-1)!
09 Jun 2004, 14:18
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I think my solution is wrong.
Assume A,B,C are the candidates and A happens to be the most beautiful
In order to make a proper judgement I need to see A at the end.
A,B,C can be arranged in 3! ways. If A comes at the end then other two come before A in 2! ways
P = 2!/3! = 1/3
In case of N P = (N-1)!/N! = 1/N
Assume A,B,C are the candidates and A happens to be the most beautiful
In order to make a proper judgement I need to see A at the end.
A,B,C can be arranged in 3! ways. If A comes at the end then other two come before A in 2! ways
P = 2!/3! = 1/3
In case of N P = (N-1)!/N! = 1/N
