document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031842>Question 1031842</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carlee (again!) is spinning a spinner marked with the letters a  through f . She defines the events A={a,b,c,d}  and B={c,d,e} . Suppose that P(a)=0.02 , P(b)=P(c)=0.1 , P(d)=0.11 , and P(e)=0.04 . <BR>\n" );
document.write( " (a)  P(A)=   <BR>\n" );
document.write( " (b)  P(B)=    <BR>\n" );
document.write( " (c)  P(A&#8745;B)=    <BR>\n" );
document.write( " (d)  P(A|B)=    <BR>\n" );
document.write( " (e)   P(B|A)=    <BR>\n" );
document.write( " (f)   Are A  and B  independent? Your answer should be \"Y\" or \"N\". </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646523 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=646523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Carlee (again!) is spinning a spinner marked with the letters a through f . She defines the events A={a,b,c,d} and B={c,d,e} . <BR>\n" );
document.write( "Suppose that <BR>\n" );
document.write( "P(a)=0.02 , <BR>\n" );
document.write( "P(b)=P(c)=0.1 , <BR>\n" );
document.write( "P(d)=0.11 , <BR>\n" );
document.write( "and P(e)=0.04 . <BR>\n" );
document.write( "(a) P(A)= 0.02+0.10 + 0.10 + 0.11 = 0.33<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "(b) P(B)= 0.10 + 0.11 + 0.04 = 0.25<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "(c) P(A&#8745;B)= P{c,d} = 0.10+0.11 = 0.21<BR>\n" );
document.write( "------------------------- <BR>\n" );
document.write( "(d) P(A|B)= P(A and B)/P(B) = 0.21/0.25<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(e) P(B|A)= P(A and B)/P(A) = 0.21/0.33<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(f) Are A and B independent? Your answer should be \"Y\" or \"N\".<BR>\n" );
document.write( "Question:: P(A|B) = P(A)*P(B) <BR>\n" );
document.write( "0.21/0.25 = 0.33*0.25<BR>\n" );
document.write( "0.84 = 0.0825<BR>\n" );
document.write( "Ans:: not equal<BR>\n" );
document.write( "Ans: A and B are not independent<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );