document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=942689>Question 942689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 1: (4 points)<BR>\n" );
document.write( "From historical data, the management of Dinny's Restaurant knows that the probability of a customer ordering a hamburger is 0.27, the probability of a customer ordering a coffee is 0.42, and probability of a customer ordering a hamburger as well as a coffee is 0.22.<BR>\n" );
document.write( "Give all answers as decimals to 4 decimal places.\r<BR>\n" );
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document.write( "(a)     What is the probability that customer will order a hamburger, a cup of coffee or both? \r<BR>\n" );
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document.write( "  Solution:     \r<BR>\n" );
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document.write( "(b)     What is the probability that customer who orders a hamburger will also order a cup of coffee?<BR>\n" );
document.write( "Solution:     <BR>\n" );
document.write( "    \r<BR>\n" );
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document.write( "(c)     What is the probability that customer who orders a cup of coffee will also order a hamburger?<BR>\n" );
document.write( "Solution:         \r<BR>\n" );
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document.write( "(d)     What is the probability that a customer orders neither a burger nor a coffee?<BR>\n" );
document.write( "Solution:      <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #574865 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=574865\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   <BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "In a restaurant, probability of a customer<BR>\n" );
document.write( "- ordering a hamburger, P(H) = 0.27<BR>\n" );
document.write( "- ordering a coffee, P(C) = 0.42<BR>\n" );
document.write( "- ordering a hamburger with a coffee, P(H&cap;C) = 0.22<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Find:<BR>\n" );
document.write( "(a) P(H&cup;C), i.e. a hamburger, a coffee or both<BR>\n" );
document.write( "(b) P(C|H), i.e. orders a coffee given she orders a hamburger<BR>\n" );
document.write( "(c) P(H|C), i.e. orders a hamburger given she orders a coffee<BR>\n" );
document.write( "(d) P(~H&cap;~C), i.e. orders neither a hamburger nor a coffee.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "(a)Given P(H)=0.27, P(H&cap;C)=0.22, and P(C)=0.42, we calculate P(H&cup;C) using the relationship<BR>\n" );
document.write( "P(H&cup;C) = P(H)+P(C)-P(H&cap;C) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.27+%2B+0.42+-+0.22+=+0.47 ALIGN=MIDDLE  ALT=\"0.27+%2B+0.42+-+0.22+=+0.47\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b)The required probability is a conditional probability, i.e.<BR>\n" );
document.write( "P(C|H) = P(C&cap;H)/P(H) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.22%2F0.27+=+22%2F27 ALIGN=MIDDLE  ALT=\"0.22%2F0.27+=+22%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) Again, it is a conditional probability, namely<BR>\n" );
document.write( "P(H|C) = P(H&cap;C)/P(C) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.22%2F0.42+=+11%2F21 ALIGN=MIDDLE  ALT=\"0.22%2F0.42+=+11%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(d) P(~H&cap;~C) = 1-P(H&cup;C) = 1-0.47 = 0.53<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "(a) probability of ordering a hamburger, a coffee or both is 0.47<BR>\n" );
document.write( "(b) probability of ordering a coffee given she orders a hamburger is 22/27<BR>\n" );
document.write( "(c) probability of ordering a hamburger given she orders a coffee is 11/21<BR>\n" );
document.write( "(d) probability of ordering neither a hamburger nor a coffee is 0.53\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );