Posted by: 3X April 6, 2008
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A beauty contest is being judged by the following rules:
1) There are N contestants not seen by the judges before the contest,
2) The contestants are individually presented to the judge 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 contestant is in the group as yet not displayed. In that case the judges would have made the wrong decision.
On the other hand, if they pass over the candidate, the contestant is disqualified from the further consideration even if it turns out that all subsequent contestants are less beautiful.
What is the probability of correctly choosing the most beautiful contestant? What is a good strategy to follow?
1) There are N contestants not seen by the judges before the contest,
2) The contestants are individually presented to the judge 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 contestant is in the group as yet not displayed. In that case the judges would have made the wrong decision.
On the other hand, if they pass over the candidate, the contestant is disqualified from the further consideration even if it turns out that all subsequent contestants are less beautiful.
What is the probability of correctly choosing the most beautiful contestant? What is a good strategy to follow?