document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001764>Question 1001764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bird breeder has a total of 50 canaries 21 of which are male and 29 of which are female.  A pet shop randomly selects 8 of them.  Find the following probabilities.  Remember to decide first if the order matters when making the solution round to six decimal places.\r<BR>\n" );
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document.write( "Question 1) What is the probability that at least six of the eight are female.  Hint at least six means either 6, or 7, or 8.\r<BR>\n" );
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document.write( "Question 2) What is the Probability that at least two of the eight are males.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618858 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=618858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> can do this by 8 choose 6 with the given probabilities of 58% and 42%<BR>\n" );
document.write( "also can do it by knowing order doesn't matter, and one form of the 28 ways can choose 6 from 8 8!/6!2!<BR>\n" );
document.write( "the six might be the first six<BR>\n" );
document.write( "29/50 *28/49*27/48*26/47*25/46*24/44*21/43*20/42.<BR>\n" );
document.write( "The denominator stays the same for all 28 ways.  The numerator is the same, too, but it is multiplied in a different order.<BR>\n" );
document.write( "28(0.58^6)(0.42)^2=0.188029<BR>\n" );
document.write( "8(0.58^7)(0.42)=0.074188 because there are only 8 ways to choose 7.<BR>\n" );
document.write( "(0.58^8)=0.012806<BR>\n" );
document.write( "The total is 0.275023<BR>\n" );
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document.write( "at least 2 are males<BR>\n" );
document.write( "do 0,1, and subtract from 1<BR>\n" );
document.write( "p(0)=p(8 females)=0.012806<BR>\n" );
document.write( "p(1)=p(7 females)=0.074188<BR>\n" );
document.write( "They add to 0.086994<BR>\n" );
document.write( "subtract from 1, because we don't want these, and get 0.913006. </SPAN>\n" );
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