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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>-----Original Message-----<br>From: extropy-chat <extropy-chat-bounces@lists.extropy.org> On Behalf Of Adrian Tymes<br>Sent: Wednesday, January 30, 2019 12:25 AM<br>To: ExI chat list <extropy-chat@lists.extropy.org><br>Subject: Re: [ExI] logic puzzle</p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>These are the ways the series could have gone down, given that information:<o:p></o:p></p><p class=MsoPlainText>BBAAA<o:p></o:p></p><p class=MsoPlainText>ABAA (series would have ended there)<o:p></o:p></p><p class=MsoPlainText>ABBAA<o:p></o:p></p><p class=MsoPlainText>ABABA<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Given that, I calculate the odds of the Bananas having won the first game as 1/4.<o:p></o:p></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>Ja, that’s what I am getting too. The authors of the test (AMC10, year 2005, problem 18) claim this:<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>If the Bananas won the first two games, the Apples would need to win the last three, so the only possible order is BBAAA.<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>If the Apples won the first game, the possible order of wins are:<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'> <o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'>ABBAA<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'>ABABA<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'>ABAAX <o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>where X means the last game wasn’t played.<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(OK, I follow them up to this point.)<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>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.<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(!)<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(Indeed?)<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(If so, I need to understand the heck outta this concept, otherwise I will miss every one of these.)<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(Adrian! Cool to see you posting again. Did you play in AMC back in your childhood and youth?)<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(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.)) <o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(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.)<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'>(spike)<o:p></o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><span style='color:black'><o:p> </o:p></span></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>On Tue, Jan 29, 2019 at 10:09 PM <<a href="mailto:spike@rainier66.com"><span style='text-decoration:none'>spike@rainier66.com</span></a>> wrote:<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> 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?<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> 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.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> If the Bananas won the second game but the Apples won the series, what is the probability that the Bananas won the first game?<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> _______________________________________________<o:p></o:p></p><p class=MsoPlainText>> extropy-chat mailing list<o:p></o:p></p><p class=MsoPlainText>> <a href="mailto:extropy-chat@lists.extropy.org"><span style='text-decoration:none'>extropy-chat@lists.extropy.org</span></a><o:p></o:p></p><p class=MsoPlainText>> <a href="http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat"><span style='text-decoration:none'>http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat</span></a><o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>_______________________________________________<o:p></o:p></p><p class=MsoPlainText>extropy-chat mailing list<o:p></o:p></p><p class=MsoPlainText><a href="mailto:extropy-chat@lists.extropy.org"><span style='text-decoration:none'>extropy-chat@lists.extropy.org</span></a><o:p></o:p></p><p class=MsoPlainText><a href="http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat"><span style='text-decoration:none'>http://lists.extropy.org/mailman/listinfo.cgi/extropy-chat</span></a><o:p></o:p></p></div></body></html>