document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196908>Question 1196908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For two events, E and F, you are given:\r<BR>\n" );
document.write( "\n" );
document.write( "P(E) = 0.30<BR>\n" );
document.write( "P(F) = 0.45<BR>\n" );
document.write( "E and F are mutually exclusive events<BR>\n" );
document.write( "What is the value of P(F | E)?  Enter your answer as a decimal rounded to two decimal places.<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 #829953 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=829953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The vertical bar means the keyword \"given\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(F | E) = P(F given E)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Mutually exclusive events are two events that have no overlap, and cannot happen simultaneously<BR>\n" );
document.write( "Because E and F are mutually exclusive, this means <BR>\n" );
document.write( "P(E and F) = 0<BR>\n" );
document.write( "aka<BR>\n" );
document.write( "P(F and E) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then we can use the conditional probability formula<BR>\n" );
document.write( "P(F given E) = P(F and E)/P(E)<BR>\n" );
document.write( "P(F given E) = 0/(0.30)<BR>\n" );
document.write( "P(F given E) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If event E happens, then we know that event F cannot happen (since they cant happen simultaneously)<BR>\n" );
document.write( "Therefore, we know P(F) is zero if we know E happened already<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );