http://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&feed=atom&action=historyChance News 50 - Revision history2014-04-21T10:16:17ZRevision history for this page on the wikiMediaWiki 1.18.1http://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=13787&oldid=prevCibes: /* The Ted Talks */2011-07-11T12:59:22Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ˇDonnelly finishes his talk by discussing how this problem has been used in his field of research DNA and the role of DNA in the courts.  He illustrates the problems of using DNA in the courts using the Sally Clark case, which we discussed in [http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_11.01.html#item2 Chance News 11.01].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ˇDonnelly finishes his talk by discussing how this problem has been used in his field of research DNA and the role of DNA in the courts.  He illustrates the problems of using DNA in the courts using the Sally Clark case, which we discussed in [http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_11.01.html#item2 Chance News 11.01].</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Contributed by Laurie Snell</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Contributed by Laurie Snell</div></td></tr>
</table>Cibeshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=13288&oldid=prevBill Peterson: /* Fraud in Iranian election? */2009-09-28T19:02:43Z<p><span class="autocomment">Fraud in Iranian election?</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Submitted by Bill Peterson, based on posts by Nancy Boynton and others to the Isolated Statisticians mailing list.<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Submitted by Bill Peterson, based on posts by Nancy Boynton and others to the Isolated Statisticians mailing list.<br></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===Update===</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">In August, Andrew Gelman's blog included a [http://www.stat.columbia.edu/~cook/movabletype/archives/2009/08/more_on_the_ira.html follow-up] on this discussion.  In particular, he provides a link to some interesting data analysis on the [http://thomaslotze.com/iran/ Iran election] by Thomas Lotze, a PhD student at the University of Maryland.  Specifically, writing on the Beber and Scacco [http://thomaslotze.com/iran/#LastDigits last digits analysis], he writes:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><blockquote>This is certainly a little bit unusual; however, we have to recognize that in their analysis, Beber and Scacco chose to remove the invalidated counts by province...if you consider all the province-level counts, the p-value goes up to just over 0.1, which is not very significant.</blockquote></ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==What’s good for the goose?==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==What’s good for the goose?==</div></td></tr>
</table>Bill Petersonhttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=9160&oldid=prevBillJefferys: /* The Ted Talks */ Sentence doesn't scan; spelling correction2009-08-28T16:32:07Z<p><span class="autocomment">The Ted Talks: </span> Sentence doesn't scan; spelling correction</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of heads and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages <del class="diffchange diffchange-inline">to </del>be about the same Peter's <del class="diffchange diffchange-inline">but </del>mathematics shows that  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of heads and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages <ins class="diffchange diffchange-inline">would </ins>be about the same<ins class="diffchange diffchange-inline">, but </ins>Peter's mathematics shows that  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH <del class="diffchange diffchange-inline">occurr </del>is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH <ins class="diffchange diffchange-inline">occurs </ins>is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In Peter's problem one player chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability of winning. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In Peter's problem one player chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability of winning. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td></tr>
</table>BillJefferyshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=8789&oldid=prevJls: /* The Ted Talks */2009-08-28T14:03:25Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of heads and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages to be about the <del class="diffchange diffchange-inline">samePeter</del>'<del class="diffchange diffchange-inline">sbut </del>mathematics shows that  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of heads and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages to be about the <ins class="diffchange diffchange-inline">same Peter</ins>'<ins class="diffchange diffchange-inline">s but </ins>mathematics shows that  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>Peter's problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In <del class="diffchange diffchange-inline">Peters </del>problem one player chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability of winning. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Peter's problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In <ins class="diffchange diffchange-inline">Peter's </ins>problem one player chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability of winning. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td></tr>
</table>Jlshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=8786&oldid=prevJls: /* The Ted Talks */2009-08-28T13:46:12Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of heads and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages to be about the <del class="diffchange diffchange-inline">same but </del>mathematics shows that  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of heads and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages to be about the <ins class="diffchange diffchange-inline">samePeter'sbut </ins>mathematics shows that  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">Peters </del>problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In Peters problem one player chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline"> Peter's </ins>problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In Peters problem one player chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability <ins class="diffchange diffchange-inline">of winning</ins>. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td></tr>
</table>Jlshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=8785&oldid=prevJls: /* The Ted Talks */2009-08-04T19:18:15Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of <del class="diffchange diffchange-inline">head </del>and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages to be about the same but mathematics shows that  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of <ins class="diffchange diffchange-inline">heads </ins>and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing the coin many times, keeping track of the average number of tosses until each of the patterns ocurr. He asks which side of the room would experience the larger average number of tosses before there pattern acurrs?  He says that most people would say that these averages to be about the same but mathematics shows that  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
</table>Jlshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=8415&oldid=prevJls: /* The Ted Talks */2009-08-04T19:15:27Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of head and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing <del class="diffchange diffchange-inline">a </del>coin many times <del class="diffchange diffchange-inline">and </del>keeping track of the average number of tosses until the <del class="diffchange diffchange-inline">pattern in question first appears</del>. <del class="diffchange diffchange-inline">Which </del>side of the room would experience the larger average number of tosses before there pattern <del class="diffchange diffchange-inline">occurs </del>?  He says that most people would say that these averages to be about the same but mathematics shows that  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of head and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing <ins class="diffchange diffchange-inline">the </ins>coin many times<ins class="diffchange diffchange-inline">, </ins>keeping track of the average number of tosses until <ins class="diffchange diffchange-inline">each of </ins>the <ins class="diffchange diffchange-inline">patterns ocurr</ins>. <ins class="diffchange diffchange-inline">He asks which </ins>side of the room would experience the larger average number of tosses before there pattern <ins class="diffchange diffchange-inline">acurrs</ins>?  He says that most people would say that these averages to be about the same but mathematics shows that  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
</table>Jlshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=8414&oldid=prevJls: /* The Ted Talks */2009-08-04T16:18:38Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Peters problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In Peters problem one chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Peters problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In Peters problem one <ins class="diffchange diffchange-inline">player </ins>chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8!  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td></tr>
</table>Jlshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=8406&oldid=prevJls: /* The Ted Talks */2009-08-04T16:13:10Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Peters problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241). Penney proposes a game in which each player chooses a pattern of the same length and then a coin is tossed a sequence of times and the player whose pattern occurs first is the winner. In Peters problem one chooses HTT and the other HTH.  From symmetry this is clearly a fair game so each has the same probability. On the other hand. as Peter says. the expected number of tosses until HTH occurs is 10 while the expected number of tosses until HTT occurs is 8! </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.  </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ˇDonnelly finishes his talk by discussing how this problem has been used in his field of research DNA and the role of DNA in the courts.  He illustrates the problems of using DNA in the courts using the Sally Clark case, which we discussed in [http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_11.01.html#item2 Chance News 11.01].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ˇDonnelly finishes his talk by discussing how this problem has been used in his field of research DNA and the role of DNA in the courts.  He illustrates the problems of using DNA in the courts using the Sally Clark case, which we discussed in [http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_11.01.html#item2 Chance News 11.01].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">Peters problem is from a well known problem called the coin tossing problem: It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241).</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
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<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.  </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
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</table>Jlshttp://test.causeweb.org/wiki/chance/index.php?title=Chance_News_50&diff=8405&oldid=prevJls: /* The Ted Talks */2009-08-04T15:48:14Z<p><span class="autocomment">The Ted Talks</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Peter's approach is to  provide a simple probability problem and then show that the method used to solve this problem also applies to real life problems.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of head and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing a coin many times and keeping track of the average number of tosses until the pattern in question first appears. Which side of the room would experience the larger average?  He says that most people would say that these averages to be about the same but mathematics shows that  </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>For his problem he assumes a coin is tossed a sequence of times and a pattern is a sequence of head and tails. He imagines assigning the pattern HTT to one half the audience and the pattern HTH to the other half.  He then imagines tossing a coin many times and keeping track of the average number of tosses until the pattern in question first appears. Which side of the room would experience the larger average <ins class="diffchange diffchange-inline">number of tosses before there pattern occurs </ins>?  He says that most people would say that these averages to be about the same but mathematics shows that  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>the expected number of tosses until the pattern HTH occurr is 10 tosses, whereas the expected number of times until the pattern  HTT occurs is 8.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ˇDonnelly finishes his talk by discussing how this problem has been used in his field of research DNA and the role of DNA in the courts.  He illustrates the problems of using DNA in the courts using the Sally Clark case, which we discussed in [http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_11.01.html#item2 Chance News 11.01].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>ˇDonnelly finishes his talk by discussing how this problem has been used in his field of research DNA and the role of DNA in the courts.  He illustrates the problems of using DNA in the courts using the Sally Clark case, which we discussed in [http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_11.01.html#item2 Chance News 11.01].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>Peters problem is from a well known problem called the coin tossing problem:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>Peters problem is from a well known problem called the coin tossing problem: <ins class="diffchange diffchange-inline">It was proposed by Walter Penny in the Journal of Recreational Mathematics (October 1969, P. 241).</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>You can also see a nice nice discussion of this problem by Martin Gardner, (1974) Mathematical games, Sci. Amer. 10, 120-125. Here you will find an elegant combinatorial solution to  this coin tossing problem, due to John Conway. This article  is also included in Gardner's book "Time Travel and Other Mathematical Bewilderments" and in some of his other books.   </div></td></tr>
</table>Jls