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A fair coin and an unfair coin


Best Answer bushindo, 11 April 2013 - 04:52 PM

Calling Dr. Bayes ... Where is Bushindo when you need him?

Spoiler for the first toss

 

On the contrary, I will, on principle, plug the number in Bayes' formula =)

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#1 BMAD

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Posted 11 April 2013 - 03:04 AM

Consider the following process. We have two coins, one of which is fair, and the other of which has heads on both sides. We give these two coins to our friend, who chooses one of them at random (each with probability 1/2). During the

rest of the process, she uses only the coin that she chose. She now proceeds to toss the coin many times, reporting the results. We consider this process to consist solely of what she reports to us.

 

Given that she reports a head on the nth toss, what is the probability that a head is thrown on the (n + 1)st toss?

 

Now assume that the process is in state "heads" on both the (n - 1)st and the nth toss. Find the probability that a head comes up on the (n + 1)st toss.

 


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#2 bonanova

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Posted 11 April 2013 - 09:51 AM

Calling Dr. Bayes ... Where is Bushindo when you need him?

Spoiler for the first toss

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 bushindo

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Posted 11 April 2013 - 04:52 PM   Best Answer

Calling Dr. Bayes ... Where is Bushindo when you need him?

Spoiler for the first toss

 

On the contrary, I will, on principle, plug the number in Bayes' formula =)

Spoiler for

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#4 BobbyGo

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Posted 11 April 2013 - 04:58 PM

Calling Dr. Bayes ... Where is Bushindo when you need him?

Spoiler for the first toss

 

I agree with your first answer, but not with your second...

 

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#5 bonanova

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Posted 11 April 2013 - 05:16 PM

Yes. I think the three of us agree that I made a mistake in the second case.
I should say the four of us. ;)
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 witzar

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Posted 12 April 2013 - 07:21 PM

If you don't like Mr Bayes, you can draw a picture.

Now all you have to do is divide green by (green+red).

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Edited by witzar, 12 April 2013 - 07:22 PM.

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#7 bonanova

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Posted 13 April 2013 - 12:06 AM

If you don't like Mr Bayes, you can draw a picture.
Now all you have to do is divide green by (green+red).

Nice diagram.

I actually get Bayes, and conditional probability (I think of it as "conditioned" probability.) And I had the right thinking and I had visualized the right numbers. And then I just wrote 5/6 when I should have written 4/5. My Bayesian aversion comes when the numbers are too large or the steps too complicated to visualize. And you just plug, plug, plug, and turn the crank. As an engineer I should love that. That's when the tool really shines. But it also robs me of the opportunity for the puzzle to shape my intuition. and that's part of my love for probability puzzles.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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