# Re: copying related probability question

Eliezer S. Yudkowsky (sentience@pobox.com)
Sun, 21 Sep 1997 15:32:45 -0500

Wei Dai wrote:
>
> [I'm new to this mailing list, so please let me know if this question is
> not appropriate.]
>
> Consider an experiment in which a volunteer subject is told the following
> by the experimenter:
>
> "You will be given a sleeping pill. After you are asleep, I will flip a
> fair coin. If the the coin lands head up, I will make an exact duplicate
> of you, place you and your clone in seperate identical rooms, and wake
> both of you up. Neither of you will be able to tell whether you are an
> original or a clone. Then I will ask both of you the following questions
>
> 1. What is the probability that you are a clone?
>
> 2. What is the probability that the coin landed head up?
>
> If the coin lands tail up, I will place you into one of the rooms
> mentioned above without making a copy of you, wake you up, and ask you the
> same questions. Also in both cases the the original (non-clone) is also
>
> 3. You are not a clone. What is the probability that the coin landed head
> up?"
>
> It seems to me that there are two possible sets of correct answers.
>
> A. 1) 1/4, 2) 1/2, 3) 1/3
>
> B. 1) 1/3, 2) 2/3, 3) 1/2

I make the odds out to be:

A. {1/4, 1/2, 1/3}.

The probability that the coin landed head up is 1/2. Since you have not been
supplied with any additional information about the actual course of events, no
factor can be altering the default probability.

Thus, the probability that you are a clone is 1/4, since there is a 1/2 chance
you were cloned and a 1/2 chance that you are the clone.

For problem three: You are not a clone. This eliminates the 1/4 probability
above. You had a 1/2 probability of being uncloned and a 1/4 probability of
being the original. You now have a 2/3 probability of being uncloned and a
1/3 probability of being the original. Thus, chances are 1/3 the coin came up heads.

```--
sentience@pobox.com      Eliezer S. Yudkowsky
http://tezcat.com/~eliezer/singularity.html
http://tezcat.com/~eliezer/algernon.html
Disclaimer:  Unless otherwise specified, I'm not telling you
everything I think I know.
```