document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328479>Question 328479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5.	(a)	A production process comprises of two separate processes, moulding and assembly.  It is known that the probability of a defect occurring in both processes is 0.03 and the probability of a defect occurring in the assembly process is 0.2.  \r<BR>\n" );
document.write( "\n" );
document.write( "(i)	If it is assumed that the occurrence of a defect is independent of the process, calculate the probability of a defect occurring in either process.\r<BR>\n" );
document.write( "\n" );
document.write( "(ii)	Calculate the probability that an item will not contain a defect.\r<BR>\n" );
document.write( "\n" );
document.write( "(iii)	If a sample of three items are selected at random from the production output, what is the probability that at least one of them will have a defect?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235403 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=235403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5. (a) A production process comprises of two separate processes, moulding and assembly. <BR>\n" );
document.write( "It is known that the probability of a defect occurring in both processes is 0.03 and the probability of a defect occurring in the assembly process is 0.2<BR>\n" );
document.write( "P(mould and assemb) = 0.03<BR>\n" );
document.write( "P(assemb) = 0.2<BR>\n" );
document.write( "Therefore P(mould) = 0.03/0.2 = 0.15<BR>\n" );
document.write( "------------------------- <BR>\n" );
document.write( "(i) If it is assumed that the occurrence of a moulding defect is independent of the defect in the assemply process, calculate the probability of a defect occurring in either process.<BR>\n" );
document.write( "P(mould OR assemb)= P(mould) + P(assemb) - P(mould AND assemb)<BR>\n" );
document.write( "= 0.15+0.2 - 0.03 = 0.32<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "(ii) Calculate the probability that an item will not contain a defect.<BR>\n" );
document.write( "P(no defect) = 1-[P(m OR p)+P(m AND p)] = 1-[0.32+0.03] = 0.65<BR>\n" );
document.write( "------------------------------------ <BR>\n" );
document.write( "(iii) If a sample of three items are selected at random from the production output, what is the probability that at least one of them will have a defect?<BR>\n" );
document.write( "0.65^3 = 0.2746<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );