document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062655>Question 1062655</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Consider the following events for a family with children:<BR>\n" );
document.write( "A = {children of both sexes}, B = {at most one boy}.<BR>\n" );
document.write( "(i) Show that A and B are independent events if a family has three children.<BR>\n" );
document.write( "(ii) Show that A and B are dependent events if a family has only two children. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677807 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=677807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3 baby possibility:<BR>\n" );
document.write( "Look at outcomes<BR>\n" );
document.write( "MMM<BR>\n" );
document.write( "MMF*<BR>\n" );
document.write( "MFM*<BR>\n" );
document.write( "MFF<BR>\n" );
document.write( "FMM*<BR>\n" );
document.write( "FFM<BR>\n" );
document.write( "FMF<BR>\n" );
document.write( "FFF<BR>\n" );
document.write( "The first three, the fifth, and the last are not allowed, probability is 3/8.  That is joint probability.<BR>\n" );
document.write( "P(first, where children of both sexes) is 3/4. The probability of the second, at most one boy, is 1/2.<BR>\n" );
document.write( "Their products is 3/8.  That is consistent with independence.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "MM<BR>\n" );
document.write( "MF<BR>\n" );
document.write( "FM<BR>\n" );
document.write( "FF<BR>\n" );
document.write( "Probability of both is 1/2.<BR>\n" );
document.write( "P(children of both sexes) is 1/2.  Probability of at most one boy is 3/4<BR>\n" );
document.write( "Their product is 3/8.  Since the joint probability is not equal to the product of each of the probabilities, they are not independent.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );