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?

thats a kind of tough , dude.

I will try to answer this more fully when I have more time.

I think the approach should be:

To simplify and unconfuse and make it boring (which is fun), let it be a distribution of numbers rather than beauties.

Say the numbers are distributed with a probability density function p(x) which is non-zero between MIN and MAX. The judges should choose a threshold based on the number of contestants still remaining to be judged. For the first candidate, let's say we start with a threshold T(1) such that the int_MIN_T(1) p(x) = 0.9 (i.e. the contestant lies in the top 10%).

There is no choice for the last one, so if we have not chosen yet... so T(N) should be MIN

Now, T(n) should be varied in such a way that probability of false detection is minimized. I think this can be solved analytically for simple systems such as uniform distribution.... more detailed analyses are welcome ( i will try this in my leisure )

I will appreciate it. I am curious to see your result and learn something from it.

Thanks!

My mathematics are good but accounts are bad.
I am not a philoshoper but the lady in the picture above is damn beautiful.
See more of her pictures (U 16 not allowed) in the following link.
http://www.apunkachoice.com/people/act895/deepika_padukone-stills1.html