document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190727>Question 1190727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that you and two friends go to a​ restaurant, which last month filled approximately 73% of the orders correctly.\r<BR>\n" );
document.write( "\n" );
document.write( "What is the probability that at least two of the three orders will be filled​ correctly? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822439 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=822439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is a binomial probability distribution problem.<BR>\n" );
document.write( "We have two outcomes: order filled correctly vs not filled correctly<BR>\n" );
document.write( "Each trial has the same probability p = 0.73 (the order being filled correctly)<BR>\n" );
document.write( "Each trial is independent of one another.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The sample size is n = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The binomial formula is<BR>\n" );
document.write( "B(k) = (nCk)*(p)^k*(1-p)^(n-k)<BR>\n" );
document.write( "B(k) = (3Ck)*(0.73)^k*(1-0.73)^(3-k)<BR>\n" );
document.write( "B(k) = (3Ck)*(0.73)^k*(0.27)^(3-k)<BR>\n" );
document.write( "where the nCk refers to the nCr combination formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now plug in k = 2 to find the probability of exactly 2 orders filled correctly<BR>\n" );
document.write( "B(k) = (3Ck)*(0.73)^k*(0.27)^(3-k)<BR>\n" );
document.write( "B(2) = (3C2)*(0.73)^2*(0.27)^(3-2)<BR>\n" );
document.write( "B(2) = (3)*(0.73)^2*(0.27)^(1)<BR>\n" );
document.write( "B(2) = 0.431649\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Repeat for k = 3<BR>\n" );
document.write( "B(k) = (3Ck)*(0.73)^k*(0.27)^(3-k)<BR>\n" );
document.write( "B(3) = (3C3)*(0.73)^3*(0.27)^(3-3)<BR>\n" );
document.write( "B(3) = (1)*(0.73)^3*(0.27)^(0)<BR>\n" );
document.write( "B(3) = 0.389017\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add up the results to find the probability of at least 2 (aka 2 or more) orders filled correctly.<BR>\n" );
document.write( "0.431649 + 0.389017 = 0.820666\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: 0.820666<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );