[ExI] logic puzzle

[Adrian Tymes]

> Since ABAAX is dependent on the outcome of 4 games instead of 5, it is twice as likely to occur and can be treated as two possibilities.

Ah, right, missed that.  So yeah, it is 1/5.

On Wed, Jan 30, 2019 at 6:55 AM <spike at rainier66.com> wrote:
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> -----Original Message-----
> From: extropy-chat <extropy-chat-bounces at lists.extropy.org> On Behalf Of Adrian Tymes
> Sent: Wednesday, January 30, 2019 12:25 AM
> To: ExI chat list <extropy-chat at lists.extropy.org>
> Subject: Re: [ExI] logic puzzle
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> These are the ways the series could have gone down, given that information:
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> BBAAA
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> ABAA (series would have ended there)
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> ABBAA
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> ABABA
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> Given that, I calculate the odds of the Bananas having won the first game as 1/4.
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> Ja, that’s what I am getting too.  The authors of the test (AMC10, year 2005, problem 18) claim this:
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> If the Bananas won the first two games, the Apples would need to win the last three, so the only possible order is BBAAA.
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> If the Apples won the first game, the possible order of wins are:
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> ABBAA
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> ABABA
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> ABAAX
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> where X means the last game wasn’t played.
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> (OK, I follow them up to this point.)
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> Since ABAAX is dependent on the outcome of 4 games instead of 5, it is twice as likely to occur and can be treated as two possibilities.
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> (!)
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> (Indeed?)
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> (If so, I need to understand the heck outta this concept, otherwise I will miss every one of these.)
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> (Adrian!  Cool to see you posting again.  Did you play in AMC back in your childhood and youth?)
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> (Sometimes when I pretend to be stoned I can kinda follow their argument (I’m not, but I can vaguely imagine what it would be like.))
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> (OK software gurus, can we make a sim to prove this?  I wrote a script that keeps telling me it is ¼, but I mighta written my own bias into the code.)
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> (spike)
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> On Tue, Jan 29, 2019 at 10:09 PM <spike at rainier66.com> wrote:
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> > I’m doing a test.  I get a different answer from the one the test publisher offers.  Anyone want to take a crack at it?
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> > The Annapolis Apples and the Boston Bananas play a series.  First team to win 3 games wins the series.  Each team is equally likely to win each game, no ties, games independent.
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> > If the Bananas won the second game but the Apples won the series, what is the probability that the Bananas won the first game?
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