document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981078>Question 981078</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a drawer has 4 red socks and 4 blue socks\r<BR>\n" );
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document.write( "a) if 2 are drawn what is the probability of a match?<BR>\n" );
document.write( "b) if 3 are drawn what is the probability of a match?<BR>\n" );
document.write( "c) What is the probability of having all one color after 4 draws?\r<BR>\n" );
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document.write( "I have this so far..<BR>\n" );
document.write( "a) 3/7  <BR>\n" );
document.write( "P (Red) on first draw = 4/8<BR>\n" );
document.write( "P (Red) on second draw = 3/7 <BR>\n" );
document.write( "4/8 * 3/7 = 12/56 <BR>\n" );
document.write( "P (Blue) is the same so<BR>\n" );
document.write( "12/56 + 12/56= 3/7\r<BR>\n" );
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document.write( "b)100% chance\r<BR>\n" );
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document.write( "c) no clue what steps to take.\r<BR>\n" );
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document.write( "Any help is appreciated!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602100 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=602100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Throughout the problem, I'm assuming no replacements are made. \r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "Case 1: You pull out a red sock on the first draw\r<BR>\n" );
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document.write( "P(drawing another red) = (# of red)/(# total)<BR>\n" );
document.write( "P(drawing another red) = 3/7\r<BR>\n" );
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document.write( "Case 2: You pull out a blue sock on the first draw\r<BR>\n" );
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document.write( "P(drawing another blue) = (# of blue)/(# total)<BR>\n" );
document.write( "P(drawing another blue) = 3/7\r<BR>\n" );
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document.write( "So either way, it's 3/7. You are correct.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "You are correct. There are only two colors. By the time you get to the third draw, you'll either pick red or blue. Either you have a match in the first two draws or you will have a match with the third draw (with one of the first two draws).\r<BR>\n" );
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document.write( "So that's why it's 100% or 1.\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "Case 1: You draw red on the first draw\r<BR>\n" );
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document.write( "P(2nd red) = 3/7<BR>\n" );
document.write( "P(3rd red) = 2/6<BR>\n" );
document.write( "P(4th red) = 1/5\r<BR>\n" );
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document.write( "P(4 reds) = (3/7)*(2/6)*(1/5)<BR>\n" );
document.write( "P(4 reds) = (3*2*1)/(7*6*5)<BR>\n" );
document.write( "P(4 reds) = 6/210<BR>\n" );
document.write( "P(4 reds) = 1/35\r<BR>\n" );
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document.write( "Case 2: You draw blue on the first draw\r<BR>\n" );
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document.write( "P(2nd blue) = 3/7<BR>\n" );
document.write( "P(3rd blue) = 2/6<BR>\n" );
document.write( "P(4th blue) = 1/5\r<BR>\n" );
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document.write( "P(4 blues) = (3/7)*(2/6)*(1/5)<BR>\n" );
document.write( "P(4 blues) = (3*2*1)/(7*6*5)<BR>\n" );
document.write( "P(4 blues) = 6/210<BR>\n" );
document.write( "P(4 blues) = 1/35\r<BR>\n" );
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document.write( "Either way, the answer is 1/35<BR>\n" );
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