document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=537176>Question 537176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A particular type of spring is manufactured by one of the two machines, A or B: 60% of the springs are made by machine A and the remainder by machine B. Of the springs manufactured, 3% are defective in some way, regardless of which machine made them. Find<BR>\n" );
document.write( "a) the probability that a spring chosen at random is manufactured by machine A and is defective;<BR>\n" );
document.write( "b) the probability that a spring chosen at random is manufactured by machine A or is defective.<BR>\n" );
document.write( "c) Use a tree diagram as a relevant technique, to find the solution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #352758 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=352758\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A particular type of spring is manufactured by one of the two machines, A or B: 60% of the springs are made by machine A and the remainder by machine B. Of the springs manufactured, 3% are defective in some way, regardless of which machine made them. Find<BR>\n" );
document.write( "a) the probability that a spring chosen at random is manufactured by machine A and is defective;<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(A and def) = P(def|A)*P(A) = 0.03*0.06 = 0.18<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "b) the probability that a spring chosen at random is manufactured by machine A or is defective.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(A OR def) = P(A) + P(def) - P(A and def)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= 0.6 + 0.03 - 0.18<BR>\n" );
document.write( "---<BR>\n" );
document.write( "= 0.63-0.18<BR>\n" );
document.write( "----<BR>\n" );
document.write( "= 0.45<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" );