document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1060190>Question 1060190</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) I have the following individual socks that are in my drawers: 6 red socks, 7 green socks, and 4 blue socks. Two socks are picked are picked out in the dark.<BR>\n" );
document.write( "a) what is the probability that if the second sock is red, then the first sock is also red? (note: we can also phrase this as \"what is the probability that the first sock was red given the seond sock is red.)<BR>\n" );
document.write( "b) what is the probability that the two socks are the same color?<BR>\n" );
document.write( "c) what is the probability that if the second socks are not red, then the first sock is blue? (this can also be phrased as \"what is the probability that the first sock was blue given that the second sock is not red(is blue or green).\") </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675161 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=675161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that the first sock was red, there are 5 red, 7 green, and 4 blue socks left.<BR>\n" );
document.write( "The probability the second sock is red is 5/16.<BR>\n" );
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document.write( "probability both are red is 6/17*(5/16)=30/272<BR>\n" );
document.write( "probability both are green is (7/17)(6/16)=42/272<BR>\n" );
document.write( "probability both are blue is (4/17)*3/16)=12/272<BR>\n" );
document.write( "That sum  is 84/272, or 21/68.<BR>\n" );
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document.write( "the possibilities are blue/blue, blue/green, green/blue, green/green, red/blue, red/green.  All denominators are 272<BR>\n" );
document.write( "B-B:12<BR>\n" );
document.write( "B-G:28<BR>\n" );
document.write( "G-B:28<BR>\n" );
document.write( "G-G:42<BR>\n" );
document.write( "R-B:24<BR>\n" );
document.write( "R-G:42<BR>\n" );
document.write( "182<BR>\n" );
document.write( "182/272.<BR>\n" );
document.write( "Of those 182, 40 are blue. The probability is 40/182=0.220<BR>\n" );
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document.write( "a rough way to check it is that the probability the first sock is blue is 4/17 or 0.235.  If we look at what the second sock can't be red, then being blue is one possibility.  If that is the case, it lessens the likelihood of the first sock's also being blue.\r<BR>\n" );
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