document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196670>Question 1196670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> DATA CHART  https://imagizer.imageshack.com/img922/1214/IzuZwz.png<BR>\n" );
document.write( "a) Find the conditional probability of survival for each type of ticket.<BR>\n" );
document.write( "​P(Survived | ​First-class)<BR>\n" );
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document.write( "enter your response here<BR>\n" );
document.write( "​P(Survived | ​Second-class)<BR>\n" );
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document.write( "enter your response here<BR>\n" );
document.write( "​P(Survived | ​Third-class)<BR>\n" );
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document.write( "enter your response here<BR>\n" );
document.write( "​P(Survived | ​Crew)<BR>\n" );
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document.write( "enter your response here<BR>\n" );
document.write( "​(Round to three decimal places as​ needed.)\r<BR>\n" );
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document.write( "Given that a passenger ​, what is the probability they had a ​-class ​ticket?<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 #829615 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=829615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The notation P(A | B) means \"P(A) given event B happened\"<BR>\n" );
document.write( "We could write like \"P(A given B)\"\r<BR>\n" );
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document.write( "So asking something like P(survived | first class) means we know the person is in first class.<BR>\n" );
document.write( "Since we can rewrite it as P(Survived given they are in first class)<BR>\n" );
document.write( "There are 220+123 = 343 such people in first class.\r<BR>\n" );
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document.write( "Of this group of 343 people, 220 survived.\r<BR>\n" );
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document.write( "Therefore, 220/343 = <font color=red>0.641 approximately</font> is the probability of a survivor given they are in first class.\r<BR>\n" );
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document.write( "We do the same thing for parts 2 through 4. <BR>\n" );
document.write( "I'll do the second part and leave parts 3 and 4 for you to do on your own. \r<BR>\n" );
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document.write( "P(survived given second-class) = (number of second-class survivors)/(number of people in second-class)<BR>\n" );
document.write( "P(survived given second-class) = (114)/(114+171)<BR>\n" );
document.write( "P(survived given second-class) = 114/285<BR>\n" );
document.write( "P(survived given second-class) = <font color=red>0.4 exactly</font>\r<BR>\n" );
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document.write( "You could write that as 0.400 or leave it as 0.4\r<BR>\n" );
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document.write( "The last part of your question is garbled and missing important info.\r<BR>\n" );
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document.write( "You wrote \"given that a passenger ____, what is the probability they had a ____ class ticket\" but forgot to fill in those blanks\r<BR>\n" );
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document.write( "I'll go over an example\r<BR>\n" );
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document.write( "Question:  given that a passenger <u> &nbsp;&nbsp;survived&nbsp&nbsp</u>, what is the probability they had a <u> &nbsp;&nbsp;first&nbsp&nbsp</u> class ticket?\r<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "There are 713 total survivors, which is the total of everything along row one (ignore the 713 in that row since it's the result of adding everything else)<BR>\n" );
document.write( "220+114+174+205 = 713\r<BR>\n" );
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document.write( "There are 220 survivors from first class (upper left corner)\r<BR>\n" );
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document.write( "The probability we get is therefore 220/713 = 0.309 approximately\r<BR>\n" );
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document.write( "If we know for certain the person is a survivor, then there's a 30.9% chance they are from first class.\r<BR>\n" );
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document.write( "Once again, this answer applies to a hypothetical example since I don't know what the full original question was. But you'll use this example template to answer your specific question. <BR>\n" );
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