document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190339>Question 1190339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A jar contains 25 marbles, 10 of which are black and 15 are white. 2 marbles are drawn WITHOUT REPLACEMENT. Find out  <BR>\n" );
document.write( "a.	The probability that both marbles drawn are white <BR>\n" );
document.write( "b.	The probability that at least one marble is black <BR>\n" );
document.write( "c.	The probability that exactly one marble is white <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 #821952 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=821952\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part A\r<BR>\n" );
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document.write( "15 white, 25 total<BR>\n" );
document.write( "m = P(1st is white) = 15/25 = 3/5<BR>\n" );
document.write( "n = P(2nd is white, given 1st is white) = 14/24 = 7/12<BR>\n" );
document.write( "P(2 white in a row) = m*n = (3/5)*(7/12) = 21/60 = 7/20\r<BR>\n" );
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document.write( "I subtracted 1 from the numerator and denominator when going from 15/25 to 14/24. This is directly due to the fact we aren't replacing the first marble.\r<BR>\n" );
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document.write( "Answer: <font color=red>7/20</font>\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "P(2 white) + P(at least one black) = 1<BR>\n" );
document.write( "P(at least one black) = 1 - P(2 white)<BR>\n" );
document.write( "P(at least one black) = 1 - 7/20<BR>\n" );
document.write( "P(at least one black) = 20/20 - 7/20<BR>\n" );
document.write( "P(at least one black) = 13/20\r<BR>\n" );
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document.write( "This works because you either get 2 white in a row, or you get at least one black marble (pick one scenario only). The two events are complementary.\r<BR>\n" );
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document.write( "Answer: <font color=red>13/20</font>\r<BR>\n" );
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document.write( "Part C\r<BR>\n" );
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document.write( "m = P(1st is white) = 15/25 = 3/5<BR>\n" );
document.write( "n = P(2nd is black, given 1st is white) = 10/24 = 5/12<BR>\n" );
document.write( "m*n = P(1st is white, 2nd is black) <BR>\n" );
document.write( "m*n = (3/5)*(5/12)<BR>\n" );
document.write( "m*n = 15/60<BR>\n" );
document.write( "m*n = 1/4\r<BR>\n" );
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document.write( "q = P(1st is black) = 10/25 = 2/5<BR>\n" );
document.write( "r = P(2nd is white, given 1st is black) = 15/24 = 5/8<BR>\n" );
document.write( "q*r = P(1st is black, 2nd is white)<BR>\n" );
document.write( "q*r = (2/5)*(5/8)<BR>\n" );
document.write( "q*r = 10/40<BR>\n" );
document.write( "q*r = 1/4\r<BR>\n" );
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document.write( "P(exactly 1 white) = m*n + q*r<BR>\n" );
document.write( "P(exactly 1 white) = 1/4 + 1/4<BR>\n" );
document.write( "P(exactly 1 white) = 2/4<BR>\n" );
document.write( "P(exactly 1 white) = 1/2\r<BR>\n" );
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document.write( "It's a coincidence that we end up with exactly 1/2. <BR>\n" );
document.write( "If the initial black and white counts were other values (say 16 black and 15 white) then the answer wouldn't be 1/2.\r<BR>\n" );
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document.write( "Answer: <font color=red>1/2</font><BR>\n" );
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