document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177193>Question 1177193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A card is elected at random from an ordinary deck of 52 playing cards. If E is the event<BR>\n" );
document.write( "that the selected card is an ace and F is the event that it is a spade, show that E and F are<BR>\n" );
document.write( "independent events.\r<BR>\n" );
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document.write( "thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805574 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=805574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "There are two ways to show that E and F are independent.  One way is to show that the probability of E given F is equal to the probability of E, and the other is to show that the probability of both E and F occurring is equal to the product of P(E) and P(F).\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(E\,|\,F)\ =\ \frac{P(E\,&\,F)}{P(F)}\ =^?\ P(E)\">\r<BR>\n" );
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document.write( "Or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(E\,&\,F)\ =^?\ P(E)\cdot P(F)\">\r<BR>\n" );
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document.write( "Using the facts that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(E)\ =\ \text{\frac{Number of Aces}{Number of Cards}}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(F)\ =\ \text{\frac{Number of Spades}{Number of Cards}}\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(E\,&\,F)\ =\ \text{\frac{Number of Aces of Spades}{Number of Cards}}\">\r<BR>\n" );
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document.write( "Do your own arithmetic.\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Solver92311&illustration_name=darwinfish.jpg\">\r<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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