document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027191>Question 1027191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A and B are independent events. If P(A and B) is 0.4 and P(A or B) is 0.9 find P(A) and P(B) where P(A) is greater than P(B)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642442 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=642442\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = P(A) and y = P(B).<BR>\n" );
document.write( "Then from the addition law of probability, \r<BR>\n" );
document.write( "\n" );
document.write( "0.9 = x+y - 0.4 ==> x+y = 1.3<BR>\n" );
document.write( "Also, since A, B are independent events, P(A&#8745;B) = P(A)P(B) = xy = 0.4\r<BR>\n" );
document.write( "\n" );
document.write( "==> x(1.3 - x) = 0.4, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+1.3x+%2B0.4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+1.3x+%2B0.4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Directly using the quadratic formula, we get the solutions x = 0.8, 0.5.\r<BR>\n" );
document.write( "\n" );
document.write( "Since x > y, it follows that P(A) = 0.8 and P(B) = 0.5. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );