document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186526>Question 1186526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 26 red cards and 26 black cards in a standard deck of playing cards, for a total of 52 cards. There are 4 kings to a deck, two of which are red kings and two of which are black kings. A card will be randomly selected from a standard deck of playing cards. Let A represent selecting a king and let B represent selecting a red card. Calculate the following probabilities:\r<BR>\n" );
document.write( "\n" );
document.write( "P (A) =\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "P (A ׀ B) =\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Based on these probabilities, are A and B independent events? Explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817502 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(A) = P(king) = 4/52 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%281%2F13%29 ALIGN=MIDDLE  ALT=\"red%281%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(A|B) = P(king|red) = P(king & red)/P(red) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F52%29%2F%2826%2F52%29+=+2%2F26+=+red%281%2F13%29 ALIGN=MIDDLE  ALT=\"%282%2F52%29%2F%2826%2F52%29+=+2%2F26+=+red%281%2F13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "So P(A) = P(A|B).  It is also easy to see that P(B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2F52++=+%282%2F52%29%2F%284%2F52%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"26%2F52++=+%282%2F52%29%2F%284%2F52%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = P(B|A).  Therefore, A and B are independent events.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Alternatively, P(A & B) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F52+=+%284%2F52%29%2A%2826%2F52%29 ALIGN=MIDDLE  ALT=\"2%2F52+=+%284%2F52%29%2A%2826%2F52%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = P(A)*P(B), and so again A and B are independent events.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );