document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203299>Question 1203299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider a box containing 3 faulty and 2 good fuses. Two fuses are chosen at random from the box. What is the probability of choosing:<BR>\n" );
document.write( "a) No faulty fuse<BR>\n" );
document.write( "b) 1 faulty fuse<BR>\n" );
document.write( "c) 2 faulty fuses<BR>\n" );
document.write( "Hence, draw the probability distribution table for event X, the number of faulty fuses obtained. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838744 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=838744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability of choosing a faulty fuse on the first try is 3/5.<BR>\n" );
document.write( "the probability of choosing a good fuse on the first tey is 2/5.<BR>\n" );
document.write( "you choose two fuses at random.\r<BR>\n" );
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document.write( "the probability of choosing two good fuses is 2/5 * 1/4 = 2/20 = 1/10.<BR>\n" );
document.write( "this is the same as choosing 0 faulty fuses.\r<BR>\n" );
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document.write( "the probability of choosing two faulty fuses is 3/5 * 2/4 = 6/20 = 3/10.\r<BR>\n" );
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document.write( "the probability of choosing one faulty fuse is (3/5 * 2/4) + (2/5 * 3/4) = 6/20 + 6/20 = 12/20 = 6/10.\r<BR>\n" );
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document.write( "the total possible combinations of getting 2 elements out of 5 elements, when 3 are faulty and 2 are good would be:\r<BR>\n" );
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document.write( "let the faulty fuses be f1, f2, and f3.<BR>\n" );
document.write( "let the good fuses be g1, g2.\r<BR>\n" );
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document.write( "you are drawing 2 fuses out of 5.\r<BR>\n" );
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document.write( "the possible combinations are:\r<BR>\n" );
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document.write( "f1 f2 = 0 good<BR>\n" );
document.write( "f1 f3 = 0 good<BR>\n" );
document.write( "f1 g1 = 1 faulty 1 good<BR>\n" );
document.write( "f1 g2 = 1 faulty 1 good<BR>\n" );
document.write( "f2 f3 = 0 good<BR>\n" );
document.write( "f2 g1 = 1 faulty 1 good<BR>\n" );
document.write( "f2 g2 = 1 faulty 1 good<BR>\n" );
document.write( "f3 g1 = 1 faulty 1 good<BR>\n" );
document.write( "f3 g2 = 1 faulty 1 good<BR>\n" );
document.write( "g1 g2 = 0 faulty\r<BR>\n" );
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document.write( "total of 0 good is 3/10<BR>\n" );
document.write( "total of 0 faulty is 1/10<BR>\n" );
document.write( "total of 1 faulty 1 good is 6/10\r<BR>\n" );
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document.write( "you could also annalyze this using combination formulas of c(n,x), where n is the total number of possibilities and x is the desired number of possibilities.\r<BR>\n" );
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document.write( "the formulas becomes:\r<BR>\n" );
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document.write( "for 0 good = c(3,2) / c(5,2) = 3/10.<BR>\n" );
document.write( "for 0 faulty = c(2,2) / c(5,2) = 1/10.<BR>\n" );
document.write( "for 1 faulty 1 good = c(3,1) * c(2,1) / c(5,2) = 6/10.\r<BR>\n" );
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document.write( "note that c(n,x) is equal to n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "as an example: c(5,2) is equal to:<BR>\n" );
document.write( "5! / (2! * 3!) which is equal to:<BR>\n" );
document.write( "(5*4*3!) / (2! * 3!) which is equal to:<BR>\n" );
document.write( "(5*4) / 2! which is equal to:<BR>\n" );
document.write( "(5*4) / (2*1) which is equal to:<BR>\n" );
document.write( "20 / 2 which is equal to:<BR>\n" );
document.write( "10\r<BR>\n" );
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document.write( "your solutions are:\r<BR>\n" );
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document.write( "a) No faulty fuse = 1/10<BR>\n" );
document.write( "b) 1 faulty fuse = 6/10<BR>\n" );
document.write( "c) 2 faulty fuses = 3/10 </SPAN>\n" );
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