document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118420>Question 118420</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321331834/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am having a hard time figuring out the solution to this problem.\r<BR>\n" );
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document.write( "A carton contains 12 eggs, 3 of which are cracked.  If we randomly select 5 of the eggs for hard boiling, what is the probability of the following events?<BR>\n" );
document.write( "a.  All of the cracked eggs are selected.<BR>\n" );
document.write( "b.  None of the cracked eggs are selected.<BR>\n" );
document.write( "c.  Two of the cracked eggs are selected.\r<BR>\n" );
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document.write( "Any help is greatly appreciated!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86539 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=86539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  carton contains 12 eggs, 3 of which are cracked. If we randomly select 5 of the eggs for hard boiling, what is the probability of the following events?<BR>\n" );
document.write( "a. All of the cracked eggs are selected.<BR>\n" );
document.write( "# of ways to pick the 3 cracked = 1<BR>\n" );
document.write( "# of ways to pick 2 others = 9C2 = [9*8]/[1*2[ = 36<BR>\n" );
document.write( "# of ways to pick 5 of 12 = 12C5<BR>\n" );
document.write( "Therefore P(3 cracked and 2 not) = [1*36]/12C5 = 36/792 = 0.0455<BR>\n" );
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document.write( "b. None of the cracked eggs are selected.<BR>\n" );
document.write( "# of ways to pick 5 not cracked = 9C5<BR>\n" );
document.write( "# of ways to pick 5 of 12 = 12C5<BR>\n" );
document.write( "Prob(5 not cracked) = 9C5/12C5 = 0.1591<BR>\n" );
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document.write( "c. Two of the cracked eggs are selected. <BR>\n" );
document.write( "# of ways to pick 2 cracked = 3C2= 3<BR>\n" );
document.write( "# of ways to pick 3 not cracked = 9C3 = 84<BR>\n" );
document.write( "# of ways to pick 5 of 12 = 12C5<BR>\n" );
document.write( "Prob(2 cracked of 5 picked) = [3*84]/12C5 = 0.3182<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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