document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990556>Question 990556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We are drawing two cards without replacement from a standard 52 card deck. Find the probability that we draw at least one black card. The probability is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610564 by </B><A HREF=/tutors/aboutme.mpl?userid=ayhseddu><B>ayhseddu(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ayhseddu><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=610564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Instead of calculating the actual probability we will first calculate the complementary probability which is the probability of drawing 0 black cards or only red cards. After we have found this complementary probability we will reduce it from 1 and thus get the required probability. \r<BR>\n" );
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document.write( "If we are drawing two cards without replacement, the total number of ways to draw cards = C(52,2)\r<BR>\n" );
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document.write( "There are a total of 26 red cards and 26 black cards.<BR>\n" );
document.write( "The number of ways to draw only red cards = C(26,2)\r<BR>\n" );
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document.write( "P(only red cards are drawn) = C(26,2)/C(52,2)= 25/102\r<BR>\n" );
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document.write( "P(at least one black card is drawn)= 1-P(only red cards are drawn) \r<BR>\n" );
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document.write( "P(at least one black card is drawn)= 1-25/102 = 77/102 = 0.75 </SPAN>\n" );
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