document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199262>Question 1199262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. In Angel’s Garden, there is a 3% chance that a tomato will be bad. Angel harvests 100 <BR>\n" );
document.write( "tomatoes and wants to know the probability that at most five tomatoes are bad.\r<BR>\n" );
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document.write( "2. Consider a rather nonstandard dice. Instead of the numbers 1 through 6, die A has two 3’s, <BR>\n" );
document.write( "two 5’s, and two 7’s; die B has two2’s, two 4’s, and two 9’s; and die C has two 1’s, two 6’s, <BR>\n" );
document.write( "and two 8’s, as in the figure below<BR>\n" );
document.write( "Suppose dice A and B are rolled. If A is more likely to get the higher number. That is, P(A > <BR>\n" );
document.write( "B) > 0.50, where {A > B} denotes the event that A beats B. Hint: Condition on the outcome of <BR>\n" );
document.write( "die A.<BR>\n" );
document.write( "Now, if B and C are rolled, B is more likely to get the higher number. And, remarkably, if C <BR>\n" );
document.write( "and A are rolled, C is more likely to get the higher number. These dice are known as nontransitive dice and are the basis of a magic trick. You pick any die. Then anyone can always <BR>\n" );
document.write( "pick a die that is more likely to beat yours. If you pick A, he picks C. If you pick B, he picks <BR>\n" );
document.write( "A. And if you pick C, he picks B. Your task is to write an R code that will simulate this nontransitive dice elaborated above.<BR>\n" );
document.write( "HINT: Define three functions that will represent the three dices as samples representing the <BR>\n" );
document.write( "three configurations given in the figure above (A, B and C), then replicate the experiment <BR>\n" );
document.write( "several times (100, or 1000 times) by calling the functions with the conditions given above.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833060 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Thank you for posting us the description of this curious phenomenon.\r<BR>\n" );
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document.write( "But it this forum we do not write computer codes in response to the visitors requests.\r<BR>\n" );
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document.write( "It is NEITHER a profile NOR a focus NOR a goal and NOR a subject of this forum.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;To learn what is the subject of this forum, <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;read attentively from the front page.\r<BR>\n" );
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document.write( "So, it was your mistake to post this request to this forum.\r<BR>\n" );
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document.write( "Try to find another web-site / forum for your request.\r<BR>\n" );
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document.write( "//////////////////\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In the future, &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28NEVER%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28NEVER%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;pack more than one problem per post - - - \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- - - if you are not an enemy to yourself &nbsp;(which I assume, &nbsp;by default) \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- - - and if you want your requests be considered seriously &nbsp;(which I also assume, &nbsp;by default).\r<BR>\n" );
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