I'll give it a try.

Let's say there are 3 contestants {A,B,C}

We have to multiply the probability of the most beautiful person {A} taking a given position by the

remaining probability of having her win the competition given that the other persons before are rejected.

Let's say A is the first person to show up.

Probability of that happening: 1/3

Probability of her being chosen: 1/1 because she is most beautiful and competition stops there

Let's say A is the second person to show up.

Probability of that happening is 1/3

Probability of her being chosen: 1/2 since this is her chance to win if the person before her is also beautiful and is chosen before her

Let's say A is the third person to show up.

Probability of that happening: 1/3

Probability of her being chosen: 1/3 since this is her chance to win if either of the 2 persons before her are chosen

Therefore, for a 3 persons competition, the probability of the most beautiful person winning would be:

=1/3*1/1 + 1/3*1/2 + 1/3*1/3

=1/3 (1 + 1/2 + 1/3) = 11/18

The general formula would simplify to:

1/n (1 + 1/2 + 1/3 + ... 1/n)

I'm not sure how to simplify this though.

_________________

Best Regards,

Paul