document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157932>Question 1157932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A drawer contains 12 red socks and 8 black socks. Suppose that you choose 2 socks at random in the dark. What is the probability that you get a pair of red socks? \r<BR>\n" );
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document.write( "A drawer contains 12 red socks and 8 black socks. Suppose that you choose 2 socks at random in the dark. What is the probability that you get a pair of black socks? \r<BR>\n" );
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document.write( "A drawer contains 12 red socks and 8 black socks. Suppose that you choose 2 socks at random in the dark. What is the probability that you do not get a pair of socks?\r<BR>\n" );
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document.write( "i missed this lesson on my google meet, hoping i can get some help, thanks\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 #780832 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I don't know what method(s) might have been taught at the meet you missed....<br><BR>\n" );
document.write( "One way to work relatively simple problems like this is to use the probabilities that each sock drawn one at a time will give the desired outcome.<br><BR>\n" );
document.write( "For getting a pair of red socks, the probability that the first is red is 12/20 and the probability the second is also red is 11/19.  The probability of a pair of red socks is then (12/20)(11/19) = 132/380.  Simplify the fraction, or express as a decimal, if necessary.<br><BR>\n" );
document.write( "Use the same method to find the probability of getting a pair of black socks.<br><BR>\n" );
document.write( "For getting two socks that don't match, you need to consider two possibilities: black then red, and red then black.<br><BR>\n" );
document.write( "P(black, red = (8/20)(12/19) = 96/380<BR>\n" );
document.write( "P(red, black) = (12/20)(8/19) = 96/380<br><BR>\n" );
document.write( "So P(unmatched pair) = 192/380<br><BR>\n" );
document.write( "Note that the three cases --  a pair of red, a pair of black, and an unmatched pair -- are all the possibilities, so the sum of the probabilities for the three cases should be 1.<br><BR>\n" );
document.write( "As problems like this get more complicated, that method quickly becomes very awkward; a more sophisticated method is much easier.<br><BR>\n" );
document.write( "Instead of calculating probabilities for each draw, we use the basic definition of probability for the whole desired outcome.<br><BR>\n" );
document.write( "For example, for drawing a pair of red socks, the probability is<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "   number of ways of drawing 2 of the 12 red socks (and 0 of the 8 black)\r\n" );
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document.write( "         total number of ways of drawing 2 of the 20 socks</PRE><BR>\n" );
document.write( "The numerator is \"12 choose 2\"; the denominator is \"20 choose 2\":<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2812%2C2%29%2FC%2820%2C2%29+=+%28%2812%2A11%29%2F2%29%2F%28%2820%2A19%29%2F2%29+=+132%2F380 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And for getting an unmatched pair, the numerator is \"12 choose 1 AND 8 choose 1\":<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%2812%2C1%29%2AC%288%2C1%29%29%2FC%2820%2C2%29+=+%2812%2A8%29%2F%28%2820%2A19%29%2F2%29+=+96%2F190 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can use this method for calculating the probability of getting a pair of red socks.<br><BR>\n" );
document.write( "Of course for each of the three outcomes, your answers should be the same by both methods.<br><BR>\n" );
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