document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100985>Question 1100985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the probabaility that a car will have a flat tire while driving through a tunnel is 0.006. Find the probability that 2 of 5000 cars passing through the tunnel will have flat tires.\r<BR>\n" );
document.write( "\n" );
document.write( "please help me with this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715570 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=715570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a binomial probability type problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula to use is p(x) = c(n,x) * p^x * q^(n-x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n is the total number of possible occurrences.<BR>\n" );
document.write( "p is the probability that one occurrence happens.<BR>\n" );
document.write( "q is the probability that one occurrence doesn't happen.<BR>\n" );
document.write( "q is equal to 1 - p.<BR>\n" );
document.write( "p^x is the probability of x occurrences happening.<BR>\n" );
document.write( "q^(n-x) is the probability of (n-x) occurrences not happening.<BR>\n" );
document.write( "c(n,x) is the number of ways you can get x occurrences out of n possible occurrences where order is not important.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in your problem:<BR>\n" );
document.write( "n is 5000.<BR>\n" );
document.write( "x is equal to 2<BR>\n" );
document.write( "n-x is equal to 5000 - 2 which is equal to 4998<BR>\n" );
document.write( "p is equal to .006<BR>\n" );
document.write( "q is equal to 1 - .006 = .994<BR>\n" );
document.write( "c(5000,2) is equal to 12497500\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula of p(x) = c(n,x) * p^x * q^(n-x) becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p(2) = c(5000,2) * .006^2 * .994^4998\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c(5000,2) = 5000! / (2! * 4998!)<BR>\n" );
document.write( "this is the same as c(5000,2) = (5000 * 4999 * 4998!) / (2! * 4998!)<BR>\n" );
document.write( "the 4998! in the numerator and denominator cancel out and you are left with:<BR>\n" );
document.write( "c(5000,2) = (5000 * 4999) / 2!<BR>\n" );
document.write( "since 2! is equal to 2, then your answer becomes:<BR>\n" );
document.write( "c(5000,2) = (5000 * 4999) / 2 and the result is:<BR>\n" );
document.write( "c(5000,2) = 12497500.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula of p(2) = c(5000,2) * .006^2 * .994^4998 becomes:<BR>\n" );
document.write( "p(2) = 12497500 * .006^2 *.994^4998 which results in:<BR>\n" );
document.write( "p(2) = 3.89291449 * 10^-11.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's a very small probability.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in decimal notation, p(2) = .0000000000389291449\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );