document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135875>Question 1135875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.19 Burger preferences:  A 2010 SurveyUSA poll asked 500 Los Angeles residents, \"What is the best hamburger place in Southern California? Five Guys Burgers? In-N-Out Burger? Fat Burger? Tommy's Hamburgers? Umami Burger? Or somewhere else?\" The distribution of responses by gender is shown below.<BR>\n" );
document.write( "(please round any numerical answers to 4 decimal places) \r<BR>\n" );
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document.write( "Male	Female	Total<BR>\n" );
document.write( "Five Guys Burgers	5	6	11<BR>\n" );
document.write( "In-N-Out Burger	162	181	343<BR>\n" );
document.write( "Fat Burger	10	12	22<BR>\n" );
document.write( "Tommy's Hamburgers	27	27	54<BR>\n" );
document.write( "Umami Burger	5	1	6<BR>\n" );
document.write( "Other	26	20	46<BR>\n" );
document.write( "Not Sure	13	5	18<BR>\n" );
document.write( "Total	248	252	500\r<BR>\n" );
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document.write( "a) Are being female and liking Five Guys Burgers mutually exclusive? \r<BR>\n" );
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document.write( "Explain:\r<BR>\n" );
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document.write( "b)What is the probability that a randomly chosen male likes In-N-Out the best? <BR>\n" );
document.write( "Incorrect <BR>\n" );
document.write( "c) What is the probability that a randomly chosen female likes In-N-Out the best? <BR>\n" );
document.write( "Incorrect <BR>\n" );
document.write( "d) What is the probability that a man and woman who are dating like In-N-Out the best? <BR>\n" );
document.write( "Incorrect <BR>\n" );
document.write( "What assumptions did you need to make? Are those assumptions reasonable? <BR>\n" );
document.write( " Incorrect \r<BR>\n" );
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document.write( "e) What is the probability that a randomly chosen person likes Umami best or that person is female? <BR>\n" );
document.write( "Incorrect\r<BR>\n" );
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document.write( "here's a screenshot of the problem with the table: https://prnt.sc/msbfhq\r<BR>\n" );
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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 #753607 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=753607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\">Part A\r<BR>\n" );
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document.write( "The events are not mutually exclusive because there are 6 females who like Five Guys Burgers best. If these two events were mutually exclusive, then this value would be 0. Mutually exclusive events are two such events where they cannot happen at the same time. \r<BR>\n" );
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document.write( "An example of mutual exclusive events would be the events \"heads\" and \"tails\" on some coin. You can only have one event happen, but not both at the same time.<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "Focus only on the male column. We have 248 total and 162 who like In-N-Out Burger best, so the probability is therefore,\r<BR>\n" );
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document.write( "162/248 = 0.65322580645161 = <font color=red size=4>0.6532</font>\r<BR>\n" );
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document.write( "It appears you have the right idea but you only put the answer accurate to two decimal places (rather than four). <BR>\n" );
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document.write( "Part C\r<BR>\n" );
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document.write( "This time we only focus on the female column<BR>\n" );
document.write( "181 females like In-N-Out Burger best<BR>\n" );
document.write( "252 females total\r<BR>\n" );
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document.write( "181/252 = 0.71825396825397 = <font color=red size=4>0.7183</font><BR>\n" );
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document.write( "Part D\r<BR>\n" );
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document.write( "Define the two events<BR>\n" );
document.write( "M = event that a male likes In-N-Out Burger best<BR>\n" );
document.write( "N = event that a female likes In-N-Out Burger best\r<BR>\n" );
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document.write( "From the previous parts (B and C), we found that<BR>\n" );
document.write( "P(M) = probability male likes In-N-Out best<BR>\n" );
document.write( "P(M) = 0.6532<BR>\n" );
document.write( "and<BR>\n" );
document.write( "P(N) = probability female likes In-N-Out best<BR>\n" );
document.write( "P(N) = 0.7183\r<BR>\n" );
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document.write( "Assuming the events M and N are independent, this would allow us to multiply the probability values<BR>\n" );
document.write( "P(M and N) = P(M)*P(N)<BR>\n" );
document.write( "P(M and N) = 0.6532*0.7183<BR>\n" );
document.write( "P(M and N) = 0.46919356<BR>\n" );
document.write( "P(M and N) = <font color=red size=4>0.4692</font>\r<BR>\n" );
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document.write( "The key thing is that the formula only works if M and N are independent. Each person surveyed is likely to not worry about what other people are doing or thinking, since they are probably alone taking it. So no single person affects any other in terms of whether they like a certain burger place. Also, a person's tastes are unique to them so even if others are present, they aren't likely to sway an opinion. The survey has a subjective base to it (ie there is no right or wrong answer). \r<BR>\n" );
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document.write( "So in short, the assumption needed to be made is that the events are independent. It's is reasonable to assume this. \r<BR>\n" );
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document.write( "Part E\r<BR>\n" );
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document.write( "252 females<BR>\n" );
document.write( "6 people like Umami Burger best<BR>\n" );
document.write( "1 person is both female and they like Umami Burger best<BR>\n" );
document.write( "252+6-1 = 257 people are either female, like Umami Burger best, or both apply\r<BR>\n" );
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document.write( "note: you subtract off that 1 person because they are in both categories, so effectively this one person is counted twice when we added the 252 and 6 together\r<BR>\n" );
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document.write( "There are 257 people we want out of 500 total, so the probability is:<BR>\n" );
document.write( "257/500= <font color=red size=4>0.5140</font><BR>\n" );
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