document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258378>Question 258378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (By way of conditional probability)<BR>\n" );
document.write( "Urn A contains 2 white and 4 red balls, whereas urn B contains 1 white and 1 red ball. A ball is randomly chosen from urn A and put in urn B, and a ball is then randomly selected from urn B. <BR>\n" );
document.write( "(a) What is the probability that the ball selected from urn B is white? <BR>\n" );
document.write( "(b) What is the conditional probability that the transferred ball was white given that a white ball is selected from urn B?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #190265 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=190265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 3 balls in B.<BR>\n" );
document.write( "1/3 of the time they are wwr and 2/3 of the time they are rrw.<BR>\n" );
document.write( "a) There are 4 possibilities:\r<BR>\n" );
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document.write( "1/3 * 2/3 = 2/9 w<BR>\n" );
document.write( "1/3 * 1/3 = 1/9 r<BR>\n" );
document.write( "2/3 * 1/3 = 2/9 w<BR>\n" );
document.write( "2/3 * 2/3 = 4/9 r<BR>\n" );
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document.write( "2/9+2/9=49 w<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "We select a white ball from B. Is it the transferred ball or the ball originally in B?<BR>\n" );
document.write( "Now our sample space is restricted to the 2/9 where a white ball is transferred and chosen and 2/9 where it was not transferred and chosen.<BR>\n" );
document.write( "So only the half where the w ball was transferred is a possibility and  the chance of selecting it is 1/2.<BR>\n" );
document.write( "1/2 * 1/2 = 1/4 the conditional probability that the transferred ball was white given that a white ball is selected from urn B.<BR>\n" );
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document.write( "Ed </SPAN>\n" );
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