document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119471>Question 119471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sirs,<BR>\n" );
document.write( "please help me regarding this problem:<BR>\n" );
document.write( " <BR>\n" );
document.write( "\"there are 3 urns containing several balls. Urn 1 has 5 white, 3 green, and 2 red balls. Urn 2 contains 1 white, 6 green and 3 red balls. Urn 3 contains 3 white, 1 green and 6 red balls. a die is tossed once. if 1 appears, a ball is drawn from urn 1. if 2 or 3 appears, a ball is drawn from urn 2. otherwise, a ball is drawn from urn 3. determine (a) the probability that a red ball is chosen, and (b) the probability that urn 3 is chosen, given that the red ball is chosen.\"\r<BR>\n" );
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document.write( "thank you very much<BR>\n" );
document.write( "sincerely,<BR>\n" );
document.write( "cebrian </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87520 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87520\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK, let's see if we can simplify it. <BR>\n" );
document.write( "Die 1, Urn 1<BR>\n" );
document.write( "Die 2, Urn 2<BR>\n" );
document.write( "Die 3, Urn 2<BR>\n" );
document.write( "Die 4, Urn 3<BR>\n" );
document.write( "Die 5, Urn 3<BR>\n" );
document.write( "Die 6, Urn 3<BR>\n" );
document.write( "Urn 1:5 W, 3 G, 2R=10 total<BR>\n" );
document.write( "Urn 2:1 W, 6 G, 3R=10 total<BR>\n" );
document.write( "Urn 3:3 W, 1 G, 6R=10 total<BR>\n" );
document.write( "where W is white, G is green, and R is red.<BR>\n" );
document.write( "a.) First, let's calculate the probability of a red ball for each urn.<BR>\n" );
document.write( "P(R/U1)=2/10<BR>\n" );
document.write( "P(R/U2)=3/10<BR>\n" );
document.write( "P(R/U3)=6/10<BR>\n" );
document.write( "P(die,1)=1/6<BR>\n" );
document.write( "P(die,2)=1/6<BR>\n" );
document.write( "P(die,3)=1/6<BR>\n" );
document.write( "P(die,4)=1/6<BR>\n" );
document.write( "P(die,5)=1/6<BR>\n" );
document.write( "P(die,6)=1/6<BR>\n" );
document.write( "P(R)=P(die,1)P(R/U1)+P(die,2)P(R/U2)+P(die,3)P(R/U2)+P(die,4)P(R/U3)+P(die,5)P(R/U3)+P(die,6)P(R/U3)<BR>\n" );
document.write( "P(R)=1/6*2/10+1/6*3/10+1/6*3/10+1/6*6/10+1/6*6/10+1/6*6/10<BR>\n" );
document.write( "P(R)=26/60=13/30<BR>\n" );
document.write( "b)We're looking for the probability of U3 given the ball is red or P(U3/R). <BR>\n" );
document.write( "Use Bayes' theorem.<BR>\n" );
document.write( "P(U3/R)=P(R/U3)P(U3)/P(R)<BR>\n" );
document.write( "P(R/U3)=6/10, from above<BR>\n" );
document.write( "P(U3)=3/6, since there are 3 chances out of 6 from the die.<BR>\n" );
document.write( "P(R)=13/30, since that was the answer to part a.<BR>\n" );
document.write( "P(U3/R)=(6/10*3/6)/(13/30)<BR>\n" );
document.write( "P(U3/R)=(6*3*30)/(6*10*13)<BR>\n" );
document.write( "P(U3/R)=9/13<BR>\n" );
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