document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172381>Question 1172381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 4 red chips and 4 blue chips. Another bag contains 2 red chips and 6 blue chips. A chip is randomly selected from one of the bags, and found to be blue. What is the probability that the chip is from the first bag? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797411 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=797411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Quick Method:<BR>\n" );
document.write( "Ignore the red chips since we know the chip is blue.\r<BR>\n" );
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document.write( "We have 4 blue chips in bag A and 6 blue chips in bag B. There are 4+6 = 10 blue chips total.\r<BR>\n" );
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document.write( "The probability the blue chip is from bag A is 4/10 = 2/5, which is the answer.\r<BR>\n" );
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document.write( "A more in-depth look:\r<BR>\n" );
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document.write( "Use the law of total probability to say that<BR>\n" );
document.write( "P(blue) = P(blue and bag A) + P(blue and bag B)<BR>\n" );
document.write( "P(blue) = P(blue, given bag A)*P(bag A) + P(blue, given bag B)*P(bag B)<BR>\n" );
document.write( "P(blue) = (4/8)*(1/2) + (6/8)*(1/2)<BR>\n" );
document.write( "P(blue) = (4/8+6/8)*(1/2)<BR>\n" );
document.write( "P(blue) = (10/8)*(1/2)<BR>\n" );
document.write( "P(blue) = 10/16<BR>\n" );
document.write( "P(blue) = 5/8\r<BR>\n" );
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document.write( "Now use conditional probability<BR>\n" );
document.write( "P(blue, given bag A) = P(bag A and blue)/P(bag A)<BR>\n" );
document.write( "P(blue, given bag A)*P(bag A) = P(bag A and blue)<BR>\n" );
document.write( "P(bag A and blue) = P(blue, given bag A)*P(bag A)\r<BR>\n" );
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document.write( "P(bag A, given blue) = P(bag A and blue)/P(blue)<BR>\n" );
document.write( "P(bag A, given blue) = P(blue, given bag A)*P(bag A)/P(blue)<BR>\n" );
document.write( "P(bag A, given blue) = (1/2)*(1/2)/(5/8)<BR>\n" );
document.write( "P(bag A, given blue) = (1/4)/(5/8)<BR>\n" );
document.write( "P(bag A, given blue) = (1/4)*(8/5)<BR>\n" );
document.write( "P(bag A, given blue) = 8/20<BR>\n" );
document.write( "P(bag A, given blue) = 2/5\r<BR>\n" );
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document.write( "If we know the chip is blue, the probability of it being from bag A is 2/5.\r<BR>\n" );
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document.write( "Answer: 2/5<BR>\n" );
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