document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=893857>Question 893857</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A garden has 8 white roses and 11 red roses. One rose is plucked from the garden and then one more rose is plucked, without replacement.\r<BR>\n" );
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document.write( "    Let the event W = plucking a white rose.<BR>\n" );
document.write( "    and event R = plucking a red rose.\r<BR>\n" );
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document.write( "In two or more complete sentences, explain the meaning of probabilities P(R/W) and P(W/R). Do they have same value? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541578 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=541578\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> garden has 8 white roses and 11 red roses.<BR>\n" );
document.write( "one rose is plucked form the garden and then one more rose is plucked with replacement.\r<BR>\n" );
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document.write( "W = event of plucking a white rose.<BR>\n" );
document.write( "R = event of plucking a red rose.\r<BR>\n" );
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document.write( "Explain the meaning of the probabilities of p(W/R) and P(R/W).<BR>\n" );
document.write( "Do they have the same value?\r<BR>\n" );
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document.write( "P(W/R) means find the probability of W given R.<BR>\n" );
document.write( "P(R/W) means find the probability of R given W.\r<BR>\n" );
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document.write( "since the two events are done without replacement, the probabilities for each will be different on the second draw than the first draw.\r<BR>\n" );
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document.write( "For the first draw, the probabilities are:\r<BR>\n" );
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document.write( "p(R) = 11/19<BR>\n" );
document.write( "p(W) = 8/19\r<BR>\n" );
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document.write( "For the second draw, the probabilities are:\r<BR>\n" );
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document.write( "p(R) given that white was plucked on the first draw = 11/18<BR>\n" );
document.write( "p(W) given that red was plucked on the first draw = 8/18\r<BR>\n" );
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document.write( "the numerator is the same as on the first draw because neither of the flowers being picked on the second draw were also picked on the first draw.\r<BR>\n" );
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document.write( "the denominator is different because there is one less flower to pluck.\r<BR>\n" );
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document.write( "the probabilities are clearly not the same.\r<BR>\n" );
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document.write( "p(R/W) = 11/18<BR>\n" );
document.write( "p(W/R) = 8/18\r<BR>\n" );
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document.write( " </SPAN>\n" );
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