document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026007>Question 1026007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose A and B are independent events in a sample space S. Given that Pr(A)=1/4 Pr(B)=1/3 Calculate Pr(A&B|AUB)\r<BR>\n" );
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document.write( "My work: I was able to get A&B to be 1/12 because I multiplied Pr(A) by the Pr(B), however I do not know how to get Pr(AUB). Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641275 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=641275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since A and B are independent, P(A&B) = P(A)*P(B) = 1/12.<BR>\n" );
document.write( "By the General Addition Law, P(AuB) = P(A) + P(B) - P(A&B) = 1/4 + 1/3 - 1/12 = 1/2.\r<BR>\n" );
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document.write( "==> P(A&B|AuB) = P((A&B)&(AuB))/P(AuB) = P(A&B)/P(AuB) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F12%29%2F%281%2F2%29+=+1%2F6 ALIGN=MIDDLE  ALT=\"%281%2F12%29%2F%281%2F2%29+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: (A&B)&(AuB) = A&B because A&B is a subset of AuB. </SPAN>\n" );
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