document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183791>Question 1183791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two people A and B are to draw alternately one ball at a time from an urn containing 3 white and 2 black balls, drawn balls not being replaced. If A takes the first turn, what is the probability that A will be the first to draw white? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814257 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the probability that A draws a white ball first is .7.\r<BR>\n" );
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document.write( "my thinking:\r<BR>\n" );
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document.write( "A gets the white ball on the first draw.<BR>\n" );
document.write( "that probability is 3/5 = .6\r<BR>\n" );
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document.write( "A gets the white ball on the second draw.<BR>\n" );
document.write( "in order for this to happen, both A and B must have drawn a black ball on their first try..<BR>\n" );
document.write( "if they do, then there are only white balls left and A is sure to draw a white ball on his second try.<BR>\n" );
document.write( "the probability of this happening is 2/5 * 1/4 * 3/3 = 6/60 = .1.\r<BR>\n" );
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document.write( "the probability that A is first to get a white ball is therefore .6 + .1 = .7.\r<BR>\n" );
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document.write( "since the total probability must be equal to 1, then the probability that B gets the white ball first must be .3.\r<BR>\n" );
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document.write( "the ways that this could happen are:\r<BR>\n" );
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document.write( "B draws a white ball on the first try.<BR>\n" );
document.write( "in order for this to happen, A must have drawn a black ball on the first try.<BR>\n" );
document.write( "the probability that B is the first to draw a white ball on the first try is therefore 2/5 * 3/4 = 6/20 = .3\r<BR>\n" );
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document.write( "B draws a white ball first on the second try.<BR>\n" );
document.write( "in order for this to happen, both A and B must have drawn a black ball on their first try.<BR>\n" );
document.write( "sine there are only white balls left, then A is assured to get a white ball on the second try.<BR>\n" );
document.write( "the probability that B gets a white ball on the second try is therefore 0.\r<BR>\n" );
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document.write( "the probabilities seem to be true.\r<BR>\n" );
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document.write( "the probability that A gets a white ball first is .7<BR>\n" );
document.write( "the probability that B gets a white ball first is .3<BR>\n" );
document.write( "the total probabilities are equal to 1.\r<BR>\n" );
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document.write( "this seems reasonable, which is why i think the probability that A gets a white ball first is .7.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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