document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=470503>Question 470503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is the question: 2 events, A and B, are defined on a sample space S such that P(A|B)= 0.6, P(At least of the events occurs)= 0.8, and P(Exactly one of the events occurs)= 0.6.  Find P(A) and P(B). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322711 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=322711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(A|B) = 0.6, <BR>\n" );
document.write( "P(A U B) = 0.8, and <BR>\n" );
document.write( "P(A) + P(B) = 0.6.<BR>\n" );
document.write( "From P(A U B) = P(A) + P(B) - P(A and B), we get P(A and B) = 0.2.\r<BR>\n" );
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document.write( "==> P(A|B) = P(A and B)/P(B), or 0.6 = 0.2/P(B), or P(B) = 0.2/0.6 = 1/3.\r<BR>\n" );
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document.write( "Hence, ==> 0.8 = P(A) + 1/3 - 0.2 ==> P(A) = 2/3. </SPAN>\n" );
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