document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201433>Question 1201433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. C. Nile and Mr. D. Mented agreed to meet at 8 P.M. in one of the Spanish restaurants in Ybor City. They were both punctual, and they both remembered the date agreed on. Unfortunately, they forgot to specify the name of the restaurant. If there are 3 Spanish restaurants in Ybor City, and the 2 men each go to 1 of these, find the probability that the following occurs. (Enter your probabilities as fractions.)\r<BR>\n" );
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document.write( "a) They meet each other.<BR>\n" );
document.write( "b) They miss each other.\r<BR>\n" );
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document.write( "Thank you!<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 #835807 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answers:<BR>\n" );
document.write( "a) <font color=red size=4>1/3</font><BR>\n" );
document.write( "b) <font color=red size=4>2/3</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "I'll refer to the persons as C and D.<BR>\n" );
document.write( "I'll also refer as the restaurants as R1,R2,R3.\r<BR>\n" );
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document.write( "Let's say C picks R1.<BR>\n" );
document.write( "D has probability <font color=red>1/3</font> of also picking R1.\r<BR>\n" );
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document.write( "This logic applies if C chose R2, or R3.<BR>\n" );
document.write( "Effectively we can make person C the anchor, and have the question be reframed to \"What are the chances person D picked the anchor restaurant?\". The order of the restaurants doesn't matter, and neither does the order of who selects first.\r<BR>\n" );
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document.write( "Therefore, the chances of them <font color=red>meeting</font> is <font color=red>1/3</font>\r<BR>\n" );
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document.write( "The chances of them <font color=red>missing</font> each other is 1 - (1/3) = <font color=red>2/3</font>\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "Form a table showing all possible combos<BR>\n" );
document.write( "C's choices are along the top<BR>\n" );
document.write( "D's choices are along the left side<BR>\n" );
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document.write( "<tr><TD ></TD><TD >R1</TD><TD >R2</TD><TD >R3</TD></tr><tr><TD >R1</TD><TD >X</TD><TD ></TD><TD ></TD></tr><tr><TD >R2</TD><TD ></TD><TD >X</TD><TD ></TD></tr><tr><TD >R3</TD><TD ></TD><TD ></TD><TD >X</TD></tr>\n" );
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document.write( "The X's refer to instances where they meet. Otherwise, they miss each other.\r<BR>\n" );
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document.write( "There are 3*3 = 9 outcomes total\r<BR>\n" );
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document.write( "There are 3 X's out of 9 slots total.<BR>\n" );
document.write( "3/9 = <font color=red>1/3</font> = chances of them <font color=red>meeting</font><BR>\n" );
document.write( "6/9 = <font color=red>2/3</font> = chances of them <font color=red>missing </font> each other.\r<BR>\n" );
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document.write( "Edit:\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "Using inspiration from the tutor @ikleyn, we can have the following<BR>\n" );
document.write( "X = P(C picks R1, D picks R1) = P(C picks R1)*P(D picks R1) = (1/3)*(1/3) = 1/9<BR>\n" );
document.write( "Y = P(C picks R2, D picks R2) = P(C picks R2)*P(D picks R2) = (1/3)*(1/3) = 1/9<BR>\n" );
document.write( "Z = P(C picks R3, D picks R3) = P(C picks R3)*P(D picks R3) = (1/3)*(1/3) = 1/9\r<BR>\n" );
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document.write( "Then X+Y+Z = (1/9)+(1/9)+(1/9) = 3/9 = <font color=red>1/3</font> represents the chances of them meeting, and <font color=red>2/3</font> is the chance of them not meeting.<BR>\n" );
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