document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909205>Question 909205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Farmer Ze'ev has four chickens-two that lay white eggs and two that lay brown eggs. If each hen has a 0.6 probability of laying an egg on any given day:<BR>\n" );
document.write( "a) What is the average number of eggs he collects each day?<BR>\n" );
document.write( "b) What is the probability of getting no eggs at all?<BR>\n" );
document.write( "c) What is the probability of getting only brown eggs (i.e, one or two, but not none)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551677 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> X~Binomial(n=6, p=0.6)<BR>\n" );
document.write( "a)  \r<BR>\n" );
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document.write( "Average = Mean = np = 6*0.6 = 3.6 eggs per day.\r<BR>\n" );
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document.write( "b) P[X=0] =  (6 choose 0)*(0.6)^0(0.4)^6 = .0041\r<BR>\n" );
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document.write( "c) X~Binomial(n=4, p=0.6) Y~Binomial(n=2, p=0.6)\r<BR>\n" );
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document.write( "P[X=0, Y=1] + P[X=0,Y=2]\r<BR>\n" );
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document.write( "P[X=0] * (P[Y=1] + P[Y=2])\r<BR>\n" );
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document.write( "(0.4)^4 * [(2 choose 1)(.6)^1*(.4)^1 + (2 choose 2)(.6)^0(.4)^2] = .0164\r<BR>\n" );
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document.write( " </SPAN>\n" );
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