document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=338902>Question 338902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a carton of eggs contains 12 eggs, 3 of which are cracked. what is the chance that when selecting five of these eggs for hard boiling, two of them are cracked? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #242954 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=242954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have 12 eggs of which 3 are cracked and 9 are not cracked.<BR>\n" );
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document.write( "P(select 5 eggs of which 2 are cracked)=9C3*3C2/12C5 <BR>\n" );
document.write( "What this means <BR>\n" );
document.write( "There are a total of 12C5 ways of selecting 5 eggs out of the 12 =792<BR>\n" );
document.write( "Of the 5 eggs selected<BR>\n" );
document.write( "There are 9C3 ways of selecting the 3 which are not cracked=84<BR>\n" );
document.write( "And 3C2 of selecting the two eggs that are cracked=3<BR>\n" );
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document.write( "So P (select 5 eggs of which 2 are cracked) =84*3/792=0.318<BR>\n" );
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document.write( "Another way to look at this<BR>\n" );
document.write( "Let C=event of selecting a cracked egg<BR>\n" );
document.write( "Let N=event of selecting a non-cracked egg<BR>\n" );
document.write( "You select 5 eggs and the probability of selecting 2 cracked eggs is <BR>\n" );
document.write( "P(CCNNN) =3/12*2/11*9/10*8/9*7/8  <BR>\n" );
document.write( "because…you have to account for the fact that the chances of each choice changes due to non-replacement of the eggs.<BR>\n" );
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document.write( "Furthermore, the event of two broken eggs out of five can happen in many different ways<BR>\n" );
document.write( "CCNNN<BR>\n" );
document.write( "NNNCC<BR>\n" );
document.write( "CNNNC<BR>\n" );
document.write( "Etc<BR>\n" );
document.write( "There are 5C2=10 ways of selecting the combination of 2 cracked eggs out of 5 eggs.<BR>\n" );
document.write( "And each of those ways has the same probability as P(CCNNN) <BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "P(select 5 eggs of which 2 are cracked)=5C2*3/12*2/11*9/10*8/9*7/8    =0.318\r<BR>\n" );
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document.write( " </SPAN>\n" );
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