document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122069>Question 1122069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Cape Town courier service promises that 80%of Johannesburg-bound parcel deliveries will reach their destinations within 12 hours. What is the probability that of the seven parcels sent at random times by a particular client in Cape Town, only one is delivered late? \r<BR>\n" );
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document.write( "I worked that out and got an answer of 0,3670. I just need help with the second part which is...\r<BR>\n" );
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document.write( "What is the probability of the seven parcels sent at random times by a particular client in Cape Town, only one is delivered within 12 hours?<BR>\n" );
document.write( "A) 0.0004<BR>\n" );
document.write( "B) 0.2753<BR>\n" );
document.write( "C) 0.2097<BR>\n" );
document.write( "D) 0.0043<BR>\n" );
document.write( "E) 0.3670\r<BR>\n" );
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document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #738116 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=738116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe this is a binomial probability type problem.<BR>\n" );
document.write( "the formula is p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "p is the probability of success.<BR>\n" );
document.write( "q is the probability of failure = 1 - p<BR>\n" );
document.write( "x is the number of successes<BR>\n" );
document.write( "n-x is the number of failures<BR>\n" );
document.write( "c(n,x) is the number of ways you can get sets of x out of a set of n where order is not important.\r<BR>\n" );
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document.write( "p = .8<BR>\n" );
document.write( "q = 1 - .8 = .2<BR>\n" );
document.write( "x = 0 to 7<BR>\n" );
document.write( "n = 7\r<BR>\n" );
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document.write( "the probability that only one is late is 1 minus the probability that 6 are on time.\r<BR>\n" );
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document.write( "that would be p(6) = .8^6 * .2 * c(7,6) = .3670016\r<BR>\n" );
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document.write( "the probability that only one is delivered on time would be:\r<BR>\n" );
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document.write( "p(1) = .8^1 * .2^6 * c(7,1) = 3.584 * 10^-4 = .0003584.\r<BR>\n" );
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document.write( "round to 4 decimal places and it equals .0004.\r<BR>\n" );
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document.write( "all the probabilities are listed below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/082904.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the sum of all probabilities is equal to 1 as it should be.\r<BR>\n" );
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document.write( "c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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