document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1078083>Question 1078083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> say that there are three defective items in a bag of 50 items. a sample of 10 items is taken at random. let a denote the number of defective items in the sample. find the probability that the sample contains <BR>\n" );
document.write( "a) exactly one defective items<BR>\n" );
document.write( "b) at least three good items;<BR>\n" );
document.write( "c) at most one defective items.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692552 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=692552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first is 3C1*47C9*10<BR>\n" );
document.write( "divided by 50C10<BR>\n" );
document.write( "This is the same as multiplying 3/50*47/49*46/48*...*39/41*10=0.3980<BR>\n" );
document.write( "Once you know there are 3 ways to choose the first, make the top and bottom of the combination add to the 50C10, which is the denominator.<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "At least 3 good items. In a sample of 10, with only three defective items, there is no way there can be fewer than 7 good items. The probability is 1.<BR>\n" );
document.write( "At most one defective item: We know the probability of 1.<BR>\n" );
document.write( "We need the probability of 0 (or subtract the probability of 2 or 3).<BR>\n" );
document.write( "probability of 0 is<BR>\n" );
document.write( "47C10/50C10=0.5041<BR>\n" );
document.write( "The sum of those two is 0.9021.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );