[ExI] logic puzzle

[spike at rainier66.com]

-----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

 

These are the ways the series could have gone down, given that information:

BBAAA

ABAA (series would have ended there)

ABBAA

ABABA

 

Given that, I calculate the odds of the Bananas having won the first game as 1/4.

 

 

 

 

 

Ja, that’s what I am getting too.  The authors of the test (AMC10, year 2005, problem 18) claim this:

 

 

 

 

If the Bananas won the first two games, the Apples would need to win the last three, so the only possible order is BBAAA.

 

If the Apples won the first game, the possible order of wins are:

ABBAA

ABABA

ABAAX 

 

where X means the last game wasn’t played.

 

(OK, I follow them up to this point.)

 

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.

 

(!)

 

(Indeed?)

 

(If so, I need to understand the heck outta this concept, otherwise I will miss every one of these.)

 

(Adrian!  Cool to see you posting again.  Did you play in AMC back in your childhood and youth?)

 

(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.))  

 

(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.)

 

(spike)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

On Tue, Jan 29, 2019 at 10:09 PM < <mailto:spike at rainier66.com> 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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