document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206803>Question 1206803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An automobile manufacturer has three factory A,B and C.They produce 50%,30% and 20% respectively of the specific model of car.30% of those produced in factory A are white,40% produced in factory B are white and 25% produced in factory C are white.<BR>\n" );
document.write( "a.if an automobile produced by the company is selected at random,find the probability that is white.<BR>\n" );
document.write( "B.Given that an automobile selected at random is white ,find the probability that it come form factory B. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844455 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=844455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> factory A produces 50% of all cars = .5<BR>\n" );
document.write( "factory B produces 30% of all cars = .3<BR>\n" );
document.write( "factory C produces 20% of all cars = .2\r<BR>\n" );
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document.write( "30% of cars produced in factory A are white = .3 * .5 = .15.<BR>\n" );
document.write( "this means that 15% of all cars produced are white and produced in factory A.\r<BR>\n" );
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document.write( "40% of cars produced in factory B are white = .4 * .3 = .12.<BR>\n" );
document.write( "this means that 12% of all cars produced are white and produced in factory B.\r<BR>\n" );
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document.write( "25% of cars produced in factory C are white = .25 * .2 = .05.<BR>\n" );
document.write( "this means that 5% of all cars produced are white and produced in factory C.\r<BR>\n" );
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document.write( "the probability that the car is white is equal to .15 + .12 + .05 = .32.<BR>\n" );
document.write( "this means that the probability that the car is white is 32%, regardless of which of the 3 factories produced it.\r<BR>\n" );
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document.write( "let D = the probability that the car is white = .32<BR>\n" );
document.write( "let E = the probability that the car is produced in factory B = .3<BR>\n" );
document.write( "let DE = the probability that the car is white and produced in factory B = .12\r<BR>\n" );
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document.write( "the probability that the car is produced in factory B given that the car is white is given by the equation p(E given D) = p(DE) / p(D) = .12 / .32 = .375.\r<BR>\n" );
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document.write( "to see how this works, take some fictitious number of cars produced and work it through, as i did in the following table that assumes 1000 cars were built in total.\r<BR>\n" );
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document.write( "50% of the cars were built in factory A = .5 * 1000 = 500<BR>\n" );
document.write( "30% of the cars were built in factory B = .3 * 1000 = 300<BR>\n" );
document.write( "20% of the cars were built in factory C = .2 * 1000 = 200\r<BR>\n" );
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document.write( "30% of the cars built in factory A were white = .3 * 500 = 150<BR>\n" );
document.write( "40% of the cars built in factory B were white = .4 * 300 = 120<BR>\n" );
document.write( "25% of the cars built in factory C were white = .25 * 200 = 50\r<BR>\n" );
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document.write( "total cars built were 1000<BR>\n" );
document.write( "total white cars built were 320.<BR>\n" );
document.write( "total cars built in factory B were 300.<BR>\n" );
document.write( "total white cars built in factory B were 120.\r<BR>\n" );
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document.write( "number of all cars built in factory B divided by total number of all cars built = 300 / 1000 = .3.\r<BR>\n" );
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document.write( "number of all white cars built in factory B divided by total number of all cars built = 120 / 1000 = .12.\r<BR>\n" );
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document.write( "number of all white cars built in factory B divided by total number of all white cars built = 120 / 320 = .375.\r<BR>\n" );
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document.write( "your solutions are:\r<BR>\n" );
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document.write( "A. if an automobile produced by the company is selected at random, find the probability that is white.\r<BR>\n" );
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document.write( "that probability is .32 = 32%.\r<BR>\n" );
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document.write( "B. given that an automobile selected at random is white, find the probability that it came from factory B.\r<BR>\n" );
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document.write( "that probability is .375 = 37.5%. </SPAN>\n" );
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