document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039599>Question 1039599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A study shows that 12% of household appliances break during any given year. If a person has 9 household appliances, what is the probability that exactly 3 of them will break next year? Round your answer to 4 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654367 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=654367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a binomial distribution problem. We'll use this formula\r<BR>\n" );
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document.write( "(n C x)*(p^x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "where in this case<BR>\n" );
document.write( "n = 9 is our sample size<BR>\n" );
document.write( "p = 0.12 is the probability of selecting a broken appliance<BR>\n" );
document.write( "x = 3 is the desired number of appliances that break<BR>\n" );
document.write( "n C x is notation referring to the combination formula.\r<BR>\n" );
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document.write( "First let's use the combination formula to compute n C x = 9 C 3.\r<BR>\n" );
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document.write( "n C x = (n!)/(x!*(n-x)!)<BR>\n" );
document.write( "9 C 3 = (9!)/(3!*(9-3)!)<BR>\n" );
document.write( "9 C 3 = (9!)/(3!*6!)<BR>\n" );
document.write( "9 C 3 = (9*8*7*6*5*4*3*2*1)/(3*2*1*6*5*4*3*2*1)<BR>\n" );
document.write( "9 C 3 = (362880)/(6*720)<BR>\n" );
document.write( "9 C 3 = (362880)/(4320)<BR>\n" );
document.write( "9 C 3 = 84\r<BR>\n" );
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document.write( "Plug that in, with the other info, to get...\r<BR>\n" );
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document.write( "(n C x)*(p^x)*(1-p)^(n-x)<BR>\n" );
document.write( "(9 C 3)*(0.12^3)*(1-0.12)^(9-3)<BR>\n" );
document.write( "(84)*(0.12^3)*(0.88)^(9-3)<BR>\n" );
document.write( "(84)*(0.12^3)*(0.88)^(6)<BR>\n" );
document.write( "(84)*(0.001728)*(0.464404086784)<BR>\n" );
document.write( "0.06740918200488\r<BR>\n" );
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document.write( "Rounding that to 4 decimal places gives 0.0674\r<BR>\n" );
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document.write( "The final answer is 0.0674<BR>\n" );
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