document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=586525>Question 586525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If b and w stand for the results of a throw of two dice, show that<BR>\n" );
document.write( "the events A = {b +w < 8} and B = {b = 3 or 4} are statistically independent<BR>\n" );
document.write( "(although it is difficult to see why they should be in the usual sense of the word) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #373776 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=373776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  If b and w stand for the results of a throw of two dice, show that<BR>\n" );
document.write( "the events A = {b +w < 8} and B = {b = 3 or 4} are statistically independent<BR>\n" );
document.write( "----<BR>\n" );
document.write( "P(A) = 5/36<BR>\n" );
document.write( "P(B) = 2/6 = 1/3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "P(A)*P(B) = (5/36)(1/3) = 5/108<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "P(A | B) = ?<BR>\n" );
document.write( "If b = 3 then w is  5 or4 or 3 or 2 or 1<BR>\n" );
document.write( "If b = 4 then w is 3 or 2 or 1<BR>\n" );
document.write( "-<BR>\n" );
document.write( "So P(A | B) = 8/36<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Since 5/108 # 8/36, A and B are independent.<BR>\n" );
document.write( "==============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );