document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473929>Question 473929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help!!!<BR>\n" );
document.write( "A class has 17 boys and 10 girls. One student is selected. F is the event of selecting a girl, and K is the event of selecting Kate, one of the girls in the class. Determine <BR>\n" );
document.write( "P(K | F)<BR>\n" );
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document.write( "P(F | K).<BR>\n" );
document.write( " (to three decimal places.)\r<BR>\n" );
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document.write( "P(K | F)=<BR>\n" );
document.write( "P(F | K)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325051 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=325051\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(K | F) literally means (in English): \"the probability of selecting Kate <u>given</u> a girl/female was selected\". I underlined \"given\" for emphasis to show that we know 100% that a girl was selected.\r<BR>\n" );
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document.write( "So if we know that a girl was selected, then what is the probability that Kate is chosen.\r<BR>\n" );
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document.write( "Take note that there are 10 girls, and only one Kate (assuming we're talking about a specific and unique \"Kate\"). So the probability is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10 ALIGN=MIDDLE  ALT=\"1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This then means that \r<BR>\n" );
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document.write( "P(K | F) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10 ALIGN=MIDDLE  ALT=\"1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In decimal form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10=0.1 ALIGN=MIDDLE  ALT=\"1%2F10=0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so \r<BR>\n" );
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document.write( "P(K | F) = 0.1\r<BR>\n" );
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document.write( "Is another way to say it. Note: 0.1 is 10%\r<BR>\n" );
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document.write( "Further notes....\r<BR>\n" );
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document.write( "If the notation P(K | F) confuses you, then think of P(K | F) as P(K) given that F has occurred (or is true). \r<BR>\n" );
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document.write( "P(F | K) is very similar, but asks the reverse: \"What is the probability of selecting a female GIVEN that Kate has been chosen?\"\r<BR>\n" );
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document.write( "Well, we know that Kate is a girl (since this is a natural assumption to make and because it's stated in the question). So because Kate was chosen and that she is a girl, we can say that the probability is 1 (basically 1 refers to 100%). In other words, if we know that Kate was selected, then the person MUST be a female.\r<BR>\n" );
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document.write( "So P(F | K) = 1\r<BR>\n" );
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document.write( " </SPAN>\n" );
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