document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263823>Question 263823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer of tire found out that 2 % of his production was defective.<BR>\n" );
document.write( "If you have just bought a new car with 4 of those tires , what is the probability that one of these tires is defective.<BR>\n" );
document.write( "thanks for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194399 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=194399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2% of production is defective.\r<BR>\n" );
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document.write( "the probability of any tire being defective is 2%.\r<BR>\n" );
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document.write( "this means that the probability of not getting a defective tire is 98%\r<BR>\n" );
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document.write( "the probability of getting 0 defective tires out of 4 tires = .98^4 = .92236815.\r<BR>\n" );
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document.write( "the probability of getting at least 1 defective tire is therefore 1 - .92236815 = .07763184.\r<BR>\n" );
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document.write( "here's how it works.\r<BR>\n" );
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document.write( "the probability of getting exactly 0 defective tires is 1 * .98^4 = :<BR>\n" );
document.write( ".92236815.<BR>\n" );
document.write( "the probability of getting exactly 1 defective tire is 4 * .02 * .98^3 = :<BR>\n" );
document.write( ".07529536<BR>\n" );
document.write( "the probability of getting exactly 2 defective tires is 6 * .02^2 * .98^2 = :<BR>\n" );
document.write( ".00230496<BR>\n" );
document.write( "the probability of getting exactly 3 defective tires is 4 * .02^3 * .98 = :<BR>\n" );
document.write( ".00003136<BR>\n" );
document.write( "the probability of getting exactly 4 defective tires is 1 * .02^4 = :<BR>\n" );
document.write( ".00000016\r<BR>\n" );
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document.write( "sum up all those probabilities and you get 1.\r<BR>\n" );
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document.write( "this is what you should get.\r<BR>\n" );
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document.write( "I summed up the numbers stored in the calculator that were not rounded so I got exactly 1.   If you add up the displayed numbers, you will get close to 1 but not right on.\r<BR>\n" );
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document.write( "your answer is:\r<BR>\n" );
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document.write( "the probability of getting at least 1 defective tire is .07763184.\r<BR>\n" );
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document.write( "the probability of getting exactly 1 defective tire is .07529536\r<BR>\n" );
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document.write( "the implicit assumption in all of this is that the manufacturer is making a very large number of tires, so that the probability can be calculated assuming replacement rather than not assuming replacement.\r<BR>\n" );
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document.write( "the multipliers in each operation are based on combination theory.\r<BR>\n" );
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document.write( "the possible number of ways of getting a set of 0 out of 4 is 1<BR>\n" );
document.write( "the possible number of ways of getting a set of 1 out of 4 is 4<BR>\n" );
document.write( "the possible number of ways of getting a set of 2 out of 4 is 6<BR>\n" );
document.write( "the possible number of ways of getting a set of 3 out of 4 is 4<BR>\n" );
document.write( "the possible number of ways of getting a set of 4 out of 4 is 1\r<BR>\n" );
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document.write( "assume your set is abcd.\r<BR>\n" );
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document.write( "there is only 1 way of getting a set of 0 out of this.<BR>\n" );
document.write( "you just don't draw any.\r<BR>\n" );
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document.write( "there is 4 ways of getting a set of 1 out of this.<BR>\n" );
document.write( "you can get a, b, c, or d.\r<BR>\n" );
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document.write( "there is 6 ways of geting a set of 2 out of this.<BR>\n" );
document.write( "you can get ab, ac, ad, bc, bd, cd\r<BR>\n" );
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document.write( "there is 4 ways of getting a set of 3 out of this.<BR>\n" );
document.write( "you can get abc, abd, acd, bcd\r<BR>\n" );
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document.write( "there is 1 way of getting a set of 4 out of this.<BR>\n" );
document.write( "you can get abcd only.\r<BR>\n" );
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document.write( "these are combinations, not permutations.   order is not important.   abc is considered the same set as acb, bac, bca, cab, cba.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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