Beauty contest

Well, if A is first or second, does that not count if she is chosen outright and second or third person is just ignored? Hence. does A need to be third for there to be a valid judgement?

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.

Hi Paul,

What you said make sense.

Anand.

The official answer is following:

P=(1/N) *SUM(from x=a+1 to N) a/(x-1)

a is crucial number of contestant in wait and see strategy

If N-> infinity P=0.37

boksana, what would be the answer for a 4 person roster? Just want to double check.

I guess this exactly says what Paul wrote just in general form, doesn't it?

Acctually, the probability will depend on a. It means on how many contestants we will ignore first, and choose the most beautiful among them.
So, Paul's general formula is wrong.

Hmmm, can you then confirm what the answer would be for a 4 person contest then? I believe that "a" was taken into consideration when I allocated the "remaining probability of having the most beautiful person win the competition given that the other persons before were rejected".

The answer will depend on your strategy. If 3 contestants were in your strategy always regected, then P=1/4.