document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206164>Question 206164</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780077312367/algebrahomeworkh>Essential Statistics in Business and Economics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Bob, Mary, and Jen go to dinner.  Each orders a different meal.  The waiter forgets who ordered which meal, so he randomly places the meals before the three diners.  Let C be the event that a diner gets the correct meal and let N be the event that a diner gets an incorrect meal.  Enumerate the sample space and then find the probability that:\r<BR>\n" );
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document.write( "a. No diner gets the correct meal<BR>\n" );
document.write( "b. Exactly one diner gets the correct meal<BR>\n" );
document.write( "c. Exactly two diners get the correct meal<BR>\n" );
document.write( "d. All three diners get the correct meal </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618409 by </B><A HREF=/tutors/aboutme.mpl?userid=waddylemons><B>waddylemons(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=waddylemons><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=618409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the answer to this problem, you first have to make a list of all the possible outcomes. Let's say Bob's meal is A, Mary's meal is B, and Jen's meal is C. The 6 possible outcomes for the order in which the waiter hands out their meals are as follows:\r<BR>\n" );
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document.write( "ABC<BR>\n" );
document.write( "ACB<BR>\n" );
document.write( "BAC<BR>\n" );
document.write( "BCA<BR>\n" );
document.write( "CAB<BR>\n" );
document.write( "CBA\r<BR>\n" );
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document.write( "If we let \"ABC\" represent the outcome where all 3 diners receive the correct meal, we can calculate the probability for the other outcomes (nobody gets the right meal, 1/3 get the correct meal, 2/3 get the correct meal).\r<BR>\n" );
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document.write( "ABC ... (everyone gets the correct meal)<BR>\n" );
document.write( "ACB ... (only Bob gets the correct meal)<BR>\n" );
document.write( "BAC ... (only Jen gets the correct meal)<BR>\n" );
document.write( "BCA ... (nobody gets the correct meal)<BR>\n" );
document.write( "CAB ... (nobody gets the correct meal)<BR>\n" );
document.write( "CBA ... (only Mary gets the correct meal)\r<BR>\n" );
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document.write( "As you can see, it's not possible for only 2 people to receive the correct meal (if someone has the wrong meal then that means they received someone else's meal...making at least 2/3 meals wrong).\r<BR>\n" );
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document.write( "We were asked to calculate the probability that:<BR>\n" );
document.write( "A. No diner gets the correct meal (2/6 = 33.3%)<BR>\n" );
document.write( "B. Exactly one diner gets the correct meal (3/6 = 50%)<BR>\n" );
document.write( "C. Exactly two diners get the correct meal (0/6 = 0.00%)<BR>\n" );
document.write( "D. All diners get the correct meal (1/6 = 16.7%) </SPAN>\n" );
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